Tuesday
July 22, 2014

Search: suppose that f is a differentiable function of x and y and g(r,s)=f(2r-s, s^2-4r). use the table of funstions to calculate gr(1,2) and gs(1,2)

Number of results: 17,566

calculus
In the following problem, suppose f(x) is continuous (and differentiable) function on the interval (0,1). Suppose also that for 0 < x<(1/4) f(x) is negative, for (1/4) <x<1 f(x) is positive, f(1/4)=0, f (2/3)=1, f ' (1/3)= 1, f ' (2/3) =3. a. If the function G(x) ...
July 3, 2009 by james

Calculus
Suppose f(x) is a differentiable function with f(-1)=2 and f(2)=-1. The differentiable function g(x) is defined by the formula g(x)=f(f(x))' A. Compute g(-1) and g(2). Explain why g(x)=0 must have at least one solution A between -1 and 2. B. Compute g'(-1) and g'(2) in terms ...
April 1, 2012 by Lin

Math--Calculus
I'm having a tough time figuring out this problem... S(x) = bracket (piecewise function) a + b arcsin*(tan x/tan 66) for 0 ≤ x < 66 24 for 66 ≤ x ≤ 90. Is the function differentiable? Why or why not? Could someone please help me? My teacher told me the ...
November 13, 2010 by Jill

Calculus
Decide if the following function f(x) is differentiable at x=0. Try zooming in on a graphing calculator, or calculating the derivative f'(0) from the definition. f(x) = x^4sin(2/x), if x is not equal to 0, and f(x) = 0 if x = 0. If it is differentiable, what is the derivative...
February 23, 2011 by Abigail

calculus
Let f be the function defined by f(x)= sqrt(x), 0 <or= x <or= 4. and f(x)= 6-x, 4 < x <or= 6 a. Is f continuous at x=4? justify. b. Find the average rate of change of f(x) on the closed interval [0,6]. c. suppose the function g(x)= k sqrt(x), 0 <or= x <or= 4...
October 8, 2012 by lisa

mean value theorem
Show that the function f(x)=1-|x|, [-1,1] does not satisfy the hypotheses of the mean value theorem on the given interval. Also how do I graph the function together with the line through the points A(a,f(a)) and B(b,f(b)). Also how do I find values of c in (a,b) that satisfy f...
October 29, 2006 by Jen

need help i don't understand
"If y is a differentialble function of u, u is a diffferentiable function of v, and v is a differentiable function of x, then dy/dx=dy/du *du/dv *dy/dx
October 5, 2013 by loli

calc again!
i got answers for this one, but i feel like i did something wrong. f(x)= 2x+1 when x is less than or equal to 2 (1/2)x^2 + k when x is greater than 2 1) what value of k will make f continuous at x = 2? my answer: i got k = 3 because it would make the two parts of the function ...
February 20, 2009 by jane

math
Suppose p(x) is a twice-differentiable function such that p(1) = 3, p'(1) = 0, and p(1) = -2. Which of the following is true? there is a relative maximum at p(1) = 3 there is a relative minimum at p(1) = 3 there is a point of inflection at p(1) = 3 none of these are true
March 11, 2014 by lilly

calc
Which of the following statements would always be true? I. If f is differentiable at x = c, then f is continuous at x = c. II. If f is continuous at x = c, then f is differentiable at x = c. III. If f is not continuous at x = c, then f is not differentiable at x = c.
December 9, 2012 by Meera

Calculus
Show that the function f(x)= x^(3) +3/(x^2) +2 has exactly one zero on the interval (-infinity, 0). So far this is what I have: 0=x^3 + 3/(x^2) +2 -2= (1/x^2)(x^5 + 3) -2x^2= x^5 +3 But now I'm stuck. I also am not sure if this is how I'm supposed to be solving the problem. We...
April 12, 2009 by Lauren

calculus
suppose that f(x) = x^3 x<=1 ax+b x>1 is differentiable at x=1 then a=?, b=?
October 20, 2012 by jul

Calculus
Assuming that f and g are functions differentiable at a (though we do not know their formulas). Prove that f +g is differentiable at a using the definition of the derivative.
October 15, 2012 by Marissa

Calculus
Suppose f and g are functions that are differentiable at x=1 and that f(1)= 2, f'(1)= -1, g(1)= -2, and g'(1)= 3. Find the value of h'(1). h(x)= [x f(x)] / [ x + g(x) ]
September 26, 2009 by Dee

Calculus
Suppose f and g are functions that are differentiable at x = 1 and that f(1) = 2, f '(1) = -1, g(1) = -2, and g '(1) = 3. Find the value of h '(1). h(x) = (x2 + 11) g(x) h '(1) =
June 13, 2013 by Mike

calc
x^2 + √(x+y) + y^2 = 0; y is a differentiable function of x
May 8, 2013 by Sunny

CACULUS
If the function f(x) is differentiable and f(x)= {ax^3 + 6x, if x≤1 {bx^2 + 4, if x>1 then a = What do I do?? No idea what's going on..
January 4, 2009 by BOB

Calculus
Sketch the graph of a function that is continuous at x=5 but not differentiable at x=5.
November 10, 2009 by Matt

Algebra
f(x) is a function differentiable at x=1 and f(1)=1/8. What is the value of f(x)-f(1) f'(x) denotes the derivative of f(x)
May 21, 2013 by Andy

Maths
f(x)is a function differentiable at x=1 and f'(1)=1/8. what is the value of f(x)-f(1) f'(x) denotes the derivative of f(x)
May 24, 2013 by Andy

MATH
Where are the functions f1(x)=|sin(x)| and f2(x) = sin(|x|) differentiable? Use n as an arbitrary integer constant.) f1(x) = |sin(x)| is differentiable for all x ≠______________ f2(x) = sin(|x|) is differentiable for all x ≠______________ No one has answered
February 11, 2013 by Selma

Math
Hey I have a question, what does is mean when a function is/not differentiable? thank you.
February 1, 2010 by Anonymous

calculus
sketch graph of a function f that is differentiable and that satisfies the following
March 24, 2011 by Anonymous

Calculus (Limits)
f(x) is a function differentiable at x=1 and f′(1)=1/13. What is the limit of (x^3 - 1)/f(x) - f(1) as x approaches 1?
July 21, 2013 by Drake

calculus (hint?)
f(x) is a twice differentiable function such that f(2x)=f(x+5)+(x−5)^2 What is f''(x)?
July 21, 2013 by andy

math
Suppose that a<b are extended real numbers and that f is differentiable on (a,b). If f' is bound on (a,b) prove f is uniformly continuous.
March 8, 2012 by sarah

Calculus
Determine whether Rolle's Theorem can be applied to f on the closed interval [a,b]. If Rolle's Theorem can be applied, find all values of c in the open interval (a,b) such that f'(x)=0. f(x) = x^(2/3) - 1 [-8,8] I plugged in both values and found out that they both equal 4 so ...
September 26, 2013 by Maddie

calculus
Describe all of the different ways a function may not be differentiable at the point P (a,f(a)).
March 3, 2010 by Anonymous

Calculus
Given f'(x)=9/2x(3x^2+2)^1/2 (this is the derivative of y= sqrt[(3x^2+2)^3]) , state any values of x for which the function is not differentiable
May 10, 2014 by Kim

math
find the numerical deriviative of the given function at the indicated point. use h=0.001. is the function differentiable at the indicated point? 4x- x^2, x=0
October 3, 2009 by joclyn

math
If g is a differentiable function such that g(x) < 0 for all real numbers x and if f'(x)=(x2-4)g(x), which of the following is true?
January 3, 2011 by nicko

Calculus
What is the state of the function f at x = 2? F(x) = [x^3 for x < 2; 5x - 2 for x > or = to 2] ?continuous or differentiable both or neither one or the other?
February 10, 2012 by Scooby10

Math
Where are the functions f1(x)=|sin(x)| and f2(x) = sin(|x|) differentiable? Use n as an arbitrary integer constant.) f1(x) = |sin(x)| is differentiable for all x ≠______________ f2(x) = sin(|x|) is differentiable for all x ≠______________
February 11, 2013 by Amka

calculus ap
If g is a differentiable function such that g(x) is less than 0 for all real numbers x and if f'(x)=(x2-4)g(x), which of the following is true?
January 2, 2011 by jane

calculus
sketch graph of a function f that is differentiable and that satisfies the following conditions:(1)f'(x)>0, when x<-5 (2)f'(x)<0, when -5<x<1 and when x>1 (3)f'(-5) =0and f'(1)=0 (4)f(-5)=6and f(1)=2.
March 24, 2011 by Anonymous

Calculus
A differentiable function f(x,y) has the property that f(2,2)=2 and fx(2,2)=1 and fy(2,2)=2. Find the equation of the tangent plane at the point on the surface z=f(x,y) where x=2, y=2.
October 17, 2012 by Caroline

Calculus
1.a)Determine dy/dx if y= sqrt[(3x^2+2)^3] For this question, I got 9/2x(3x^2+2)^1/2 as my answer. b)State any values of x for which the function is not differentiable
May 9, 2014 by Kim

calculus
If y is a differentiable function of x, then the slope of the tangent to the curve xy - 2y + 4y^2 = 6 at the point where y=1 is ...... How do I do this? Thanks. xy - 2y + 4y^2 = 6 ---> d[xy - 2y + 4y^2] = 0 ---> xdy + ydx - 2dy + 8ydy = 0 ---> (x + 8y - 2)dy/dx = -y...
December 3, 2006 by Jen

maths
prove that the following function is differentiable at x=0 using first principles: f(x)= e^x when x<0 x=1 when x>0 or x=0 also is f(x) differntiable for all real x?
December 1, 2009 by kobe

Calculus
Suppose you have a rational function that its denominator is (X-c) and numerator can be any function. Suppose you need to find the limit of this rational function given as x goes to value c. Can you always say that for this problem the limit does not exist?
January 22, 2012 by Cody

math
Suppose you have a rational function that its denominator is (X-c) and numerator can be any function. Suppose you need to find the limit of this rational function given as x goes to value c. Can you always say that for this problem the limit does not exist?
January 22, 2012 by Codster

Calculus
It is given that a differentiable function f(x)=4x^3+kx^2-36x-15 (k is a constant) is decreasing on -3/2<x<2 and increasing on 2<x<5. Find the value of k and the turning point(s) of the curve y=f(x).
November 9, 2012 by Anonymous

Real Analysis
a) Give an example of a function, whose limit exists as x approaches 2, but it is not continuous at x=2 b)Give an example of a function that is not differentiable at x=2, but it is continuous at x=2
June 9, 2010 by Akkie

Calculus (Continuity and Differentiability)
Okay. So I am given a graph of a derivative. From what I can gather, it looks like the function might be abs(x-2)-4. (I was not given an explicit function for g', just its graph.) The question then goes on to ask me: Is it possible, impossible, or certain that the function g ...
November 12, 2011 by Mishaka

Calculus Help Please!!!
Consider the function f(x)= x −1≤ x< 0 f(x)=tan(x) 0≤ x ≤ π/4 a. Draw a neat sketch of this function. b. Is f(x) continuous at x = 0? (Justify your answer.) c. Is f(x) differentiable at x = 0? (Justify your answer.) show steps! Thanks!
April 8, 2014 by Anonymous

Calculous
let f be the function defined by |x-1|+2 for X<1 f(x)= ax^2-Bx, for X>or equal to 1. where a and b are constants a)if a=2 and b=3 is f continious for all x? justify your answer b)describe all the values of a and b for which f is a continious function c) For what values ...
November 21, 2011 by Yoona

AP Calculous
let f be the function defined by |x-1|+2 for X<1 f(x)= ax^2-Bx, for X>or equal to 1. where a and b are constants a)if a=2 and b=3 is f continious for all x? justify your answer b)describe all the values of a and b for which f is a continious function c) For what values ...
November 21, 2011 by Yoona

math
Suppose that function f:[0,2]->R is continuous at [0,2], differentiable at (0,2) and such that f(0)=0, f(1)=1 and f(2)=1. a) Show that there is a x1 that belongs to (0,1) such that f'(x1)=1. b) Show that there is a x2 that belongs to (1,2) such that f'(x2)=0. c) Show that ...
January 16, 2013 by Zisis

calculus
Consider the function f(x) = piecewise [(x^3)(cos(1/x)) , x=/=0], [0, x=0]. Use the definition of the derivative at a point to determine if f is differentiable at x=0 I am not sure how to start this question. Am I supposed to plug in x = 0?
January 29, 2012 by Daniel

Calculus
Suppose that p(x) is the density function for heights of American men, in inches, and suppose that p(69)=0.22. Think carefully about what the meaning of this mathematical statement is. (a) Approximately what percent of American men are between 68.7 and 69.3 inches tall? b) ...
October 27, 2011 by Cesar

Calculus
Suppose that p(x) is the density function for heights of American men, in inches, and suppose that p(69)=0.22. Think carefully about what the meaning of this mathematical statement is. (a) Approximately what percent of American men are between 68.7 and 69.3 inches tall? b) ...
October 28, 2011 by Cesar

Calculus
1. For a differentiable function f, f' be the funcyion defined by f'(x) lim h->0 =f(x+h)-f(x-h)/(h) a: Determine f'(x) for f(x)=x b: Determine f'(x) for f(x)=x^2
October 29, 2012 by Rudy

Calculus
find all values of x for which function is differentiable. y=lnx^2 why is the answer= for all x doesn't equal 0?
October 29, 2010 by Jin

Calculus
Identify any x-values at which the absolute value function f(x) = 6 |x + 7|, is not continuous: x = _____ not differentiable: x = _____
February 23, 2011 by Cesar

another graph - complicated
Sketch the graph of a differentiable function y = f(x) with the following properties. f(2) = 3, f'(2) = 0, and (a) f'(x) > 0 for x < 2, f'(x) < 0 for x > 2 (b) f'(x) < 0 for x < 2, f'(x) > 0 for x > 2 (c) f'(x) < 0 for x not equalt to 2 (d) f'(x) >...
November 5, 2006 by Jen

Calculus
Given that f is a differentiable function with f(2,5) = 6, fx(2,5) = 1, and fy(2,5) = -1, use a linear approximation to estimate f(2.2,4.9). The answer is supposed to be 6.3. Here's what I've done so far: L(x,y) = f(2,5) + fx(2,5)(x) + fy(2,5)(y) L(x,y) = 6 + x - y L(2.2,4.9...
September 30, 2012 by James

Calc
Suppose Y1 is a function of x which dy1/dx=3y1. Suppose y2 is a function of x which dy2/dx=8x+5. If the graphs of y1 and y2 have the same y-intercept and they intersect at x=2, then determine the value of the y-intercept.
October 11, 2011 by Andres

calculus
Let f be a differentiable function such that f(3) = 2 and f'(3) = 5. If the tangent line to the graph of f at x = 3 is used to find an approximation to a zero of f, that approximation is? So confused
April 21, 2011 by Matt

calculus
The function f is twice differentiable, and the graph of f has no points of inflection. If f(6)+3, f'(6)=-1/2, and f"(6)=-2, which of th following could be the value of f(7). A.)2 B.)2.5 C.)2.9 D.)3 E.)4 the answer is A. but what are the steps to reach this answer?
April 26, 2011 by Confused

Calc ii
Let f be twice differentiable with (f(0)=4), (f(1)=8), and (f'(1)=6). Evaluate the integral from 0 to 1 of xf''(x)dx\). I have no clue how to approach this since we dont know what the function is? please help, I've finished every other question and the assignemnt is due at 9
October 4, 2013 by Anonymous

Math
suppose u and v are functions of x that are differentiable at x=2 and that u(2) =3, u'(2) = -4, v(2) = 1, and v'(2) find values of derivatives at x = 2 (d/dx)(uv) = ? I would like to know how to set this up because I'm only used to getting problems that want the d/dx given ex...
November 1, 2011 by Amy

math
Thank you for your help :) "The piecewise function f(x)= n(x^3)-x______when____x<(or=to)1 =m(x^2)+5_______when_____x>(or=to)1 is differentiable everywhere. What is n? If you could explain step by step how to do this that would be great because I just do not see how to do...
January 17, 2011 by APPRECIATIVE STUDENT

Calculus
I need help creating an equation for a piecewise defined function with two different rules, that is continuous but not differentiable at the point where the rules change, x=3. Please help to justify the answer.
October 20, 2010 by Kelly

Maths Derivatives & Calulus
1) Find d^2y / dx^2 given that y^3 - x^2 = 4 2)If y = x + ( 1 / x ) , prove that x^2 . y'' + xy' a^2 . y = 0 3) Find dy/dx for the following function. cos ( x - y ) = ( y ) ( 2x + 1 ) ^3 4)Find the values of A and B that make f(x) differentiable at x = 0 f(x) = A + 2x + 3...
October 21, 2011 by Yousef

Craig - baloon - calculus moved up
Posted by Craig on Tuesday, November 25, 2008 at 7:54pm. t: 0 2 5 7 11 12 r'(t): 5.7 4.0 2.0 1.2 0.6 0.5 The volume of a spherical hot air balloon expands as the air inside the balloon is heated. The radius of the balloon in feet is modeled by a twice-differentiable function ...
November 26, 2008 by Damon

Last two CALC questions. :)
8. If f(x) = sin(7 − 5x), find f′(π), which is the derivative at π: −0.754 −0.657 0 * 0.657 3.770 9. Given the function: g(x)={x+b, x<0 {cos(x), x≥0 Find the value of b, if any, that will make the function differentiable at x = 0. 0 1...
December 20, 2013 by Samantha

Calculus
Sketch a graph of a function f(x) that is differentiable and that satisfies the following conditions. c) f'(-3) = 0 and f'(1) = 0 Please show me, step by step, how to sketch the problem!
May 25, 2008 by Anonymous

math
I dont understand this calculus problem at all. can someone show me step by step? Find all values of x for which the function is differentiable
October 3, 2009 by alison

math, please somebody help me
Given the function f(x) = x4 , and suppose g(x) is some other function of x. (a) Then the function F(x) = (g(x))^4 is the same thing as ... a. f '(g(x)) g'(x) b. f(g(x)) c. f '(x) d. f '(g(x)) e. g(f(x)) (b) By either the extended power or the chain rule, we have F '(x) = a...
February 20, 2007 by jessica (the other one)

math
Hi would you please show how to know if the function is differentiable or not ? please show me the answer with examples
December 13, 2011 by jack

Calculus, check my answers, please!
Could someone tell me if I'm right, and if not what the correct answer is? Thank you! I'd appreciate an explanation, too, if you could. :) 1. Suppose you're given the following table of values for the function f(x),and you're told that the function is even: x f(x...
October 2, 2013 by Samantha

economics
Suppose a monopolist faces production function Q = 3KL and demand function Q = 12 − P. Derive the input demand (as a function of Q, r and w) for capital and labor.
March 31, 2011 by Yash

calculus 2
Suppose that you can calculate the derivative of a function using the formula f'(x) = 4f(x) + 2x. If the output value of the function at x= 4 is 2 estimate the value of the function at 4.013
November 15, 2009 by rimmel

Precalculus
Suppose f is a function with exponential decay. Explain why the function g defined by g(x)=1/f(x) is a function with exponential growth. PLEASE HELP!!
March 10, 2010 by jh

Calc
Various values for the derivative, f'(x), of a differentiable function f are shown below. x=1, f'(x) = 8 x=2, f'(x) = 4 x=3, f'(x) = 0 x=4, f'(x) = -4 x=5, f'(x) = -8 x=6, f'(x) = -12 If f'(x) always decreases, then which of the following statements must be true? A) f(x) has a...
January 21, 2011 by Erica

Calculus, check my answers, please! 3
Did I get these practice questions right? 1. Suppose that f is an even function whose domain is the set of all real numbers. Then which of the following can we claim to be true? ***The function f has an inverse f 1 that is even. The function f has an inverse f 1, but we can'...
October 2, 2013 by Samantha

How to sketch graph of...
a differentiable function y =f(x) that has the given properties. 1. local minimum at (1,1), and local maximum at (3,3) 2. local minima at (1,1) and (3,3) 3. local maxima at (1,1) and (3,3) I don't remember how to do this. Thank you. http://en.wikipedia.org/wiki/...
November 3, 2006 by Jen

Calculus
I don't understand what the graph is suppose to show and what the integral equation is suppose to mean. How would I use the graph to answer the questions? f is the differentiable function whose graph is shown in the figure. The position at time t (sec) of a particle moving ...
May 20, 2007 by Anonymous

one more graph question
Hopefull the last one. :) Sketch the graph of a differentiable function y = f(x) with this property: A local minimum value that is greater than one of its local maximum values
November 5, 2006 by Jen

Calculus
Suppose that you can calculate the derivative of a function using the formula f(x) = 2f(x) + 4x. If the output value of the function at x=4 is 3 estimate the value of the function at 4.012. Linear Approximation right? I'm not seeing an f'(x) anywhere. Can you retype your ...
October 14, 2006 by Michael

Micro econ
1: Suppose John had a utility function of U=X^2/3Y^1/3 . Derive Johns demand function from his utility function showing all the necessary steps. i know that the MUx=MUy and first i derive the equation to 2/3X^-1/3 1/3Y^-2/3 then im stuck i need help with the simplification
September 18, 2007 by Brett

Calculus
Can someone prove (informally) the following theory: If there is a differentiable function, f, that is represented by a Taylor series, T, then the convergence interval for series T is identical to the convergence interval for the term-by-term derivative T'.
June 22, 2009 by Sean

precalculus
Suppose f is an even function and g is an odd function such that the composition fog is defined.d show that fog is an even function
September 23, 2012 by Fatima

Check a few more CALC questions, please?
I feel pretty good on my answers. Are there any I got wrong? Thank you for the help! 1. If g(x) = tan (5x^2), then g′(x) = * 10x sec2(5x2) sec2(5x2) 10xsec(5x2)tan(5x2) 10sec2(5x2) 7xsec2(5x2) 2. The inflection point of the curve y = x4 − 8x3 + 24x2 + 7x − 3...
December 19, 2013 by Samantha

Math -- Calculus
Hours of Daylight as a Function of Latitude Let S (x) be the number of sunlight hours on a cloudless June 21, as a function of latitude, x, measured in degrees. (a) What is S (0)? (b) Let x0 be the latitude of the Arctic Circle (x0 ≈ 66◦ 30′ ). In the ...
October 10, 2008 by Gerald

Algebra
Suppose H(x)=(sqrt5x+3). Find two functions f and g such that (fog)(x)= H(x) . f(x)= g(x)= Neither function can be the identity function. (There may be more than one correct answer.)
February 4, 2011 by Janet

precalculus
Suppose g is an even function and f is any function such that the composition fog is defined. show that fog is an even function
September 23, 2012 by Fatima

calc
Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers "c" that satisfy the conclusion of Rolle's Theorem. f(x)=sin4pix , [-1/2,1/2] Well according to Rolle's Theorem, it has to be continuous on [a.b] and it is ...
April 14, 2007 by Julia

pre calc
The Identity Function The Squaring Function The Cubing Function The Reciprocal Function The Square Root Function The Exponential Functional Lo The Natural Logarithum Function The Sine Function The Cosine Function The Absolute Value Function The Greatest Integer Function The ...
December 18, 2009 by kim

calculus
If g is a differentiable function such that g(x) is less than 0 for all real numbers x and if f'(x)=(x2-4)g(x), which of the following is true? f has a relative maximum at x=-2 and a relative minimum at x=2, f has a relative minimum at x=-2 and has a relative maximum at x=2, f...
January 2, 2011 by felix

differentiability
If g is a differentiable function such that g(x) is less than 0 for all real numbers x and if f prime of x equals (x2-4)*g(x), which of the following is true? A. f has a relative maximum at x=-2 and a relative minimum at x=2, B. f has a relative minimum at x=-2 and a relative ...
December 31, 2010 by matthew

Calculus
Suppose f(x) is differentiable at x=a. What does tangent line approximation, y=, mean? Select all that apply (A) Local linearization (B) y=f(x)-f(a)-f'(a)(x-a) (C) The best liner approximation of f(x) near a (D) After zooming y is a good approxiamtion to f(x) (E) f(x)~y=f(a...
November 5, 2008 by George

Calculus
Suppose f(x) is differentiable at x=a. What does tangent line approximation, y=, mean? Select all that apply (A) Local linearization (B) y=f(x)-f(a)-f'(a)(x-a) (C) The best liner approximation of f(x) near a (D) After zooming y is a good approxiamtion to f(x) (E) f(x)~y=f(a...
November 5, 2008 by George

Calculus
Suppose f(x) is differentiable at x=a. What does tangent line approximation, y=, mean? Select all that apply (A) Local linearization (B) y=f(x)-f(a)-f'(a)(x-a) (C) The best liner approximation of f(x) near a (D) After zooming y is a good approxiamtion to f(x) (E) f(x)~y=f(a...
November 5, 2008 by George

Calculus
Suppose f(x) is differentiable at x=a. What does tangent line approximation, y=, mean? Select all that apply (A) Local linearization (B) y=f(x)-f(a)-f'(a)(x-a) (C) The best liner approximation of f(x) near a (D) After zooming y is a good approxiamtion to f(x) (E) f(x)~y=f(a...
November 5, 2008 by George

Calculus
Let f be a twice-differentiable function such that f(2)=5 and f(5)=2. Let g be the function given by g(x)= f(f(x)). (a) Explain why there must be a value c for 2 < c < 5 such that f'(c) = -1. (b) Show that g' (2) = g' (5). Use this result to explain why there must be a ...
February 7, 2011 by Leanna

Calculus c
Let f be a twice-differentiable function defined on the interval -1.2 less than or equal to x less than or equal to 3.2 with f(1)=2. The graph of f', the derivative of f, is shown on the right. The graph of f' crosses the x-axis at x=-1 and x=3 and has a horizontal tangent at ...
December 19, 2012 by Madeline

statistics
Suppose that a random variable Y has a probability density function given by f(y) = ( ky 3 e y=2 ; y > 0 0; elsewhere: Find the value of k that makes f(y) a density function.
April 16, 2012 by Anonymous

URGENT!! PLEASE Calc
Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers "c" that satisfy the conclusion of Rolle's Theorem. f(x)=sin4pix , [-1/2,1/2] Well according to Rolle's Theorem, it has to be continuous on [a.b] and it is ...
April 14, 2007 by Julia

economics
Suppose a person has a utility function U=YX. What is the minimum level of income required to get a utility of 20? Your answer should be a function of, among other things, Px and Py.
September 20, 2007 by jon

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