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 (x24)*g(x), which of the following is true? A. f has a relative maximum at x=2
22,638 results
PreCalculus
A rectangle is bounded by the xaxis and the semicircle y = √36 – x2, as shown in the figure below. Write the area A of the rectangle as a function of x, and determine the domain of the area function. A = all real numbers except x = 36 all real numbers

calculus
f (x)={cx+d for x≤2 {x^2−cx for x>2 Let f be the function defined above, where c and d are constants. If f is differentiable at x=2, what is the value of c+d ? 4, 2, 0, 2, 4

Calculus
At x = 3, the function given by f(x) = { x² , x

calculus
Suppose f is a onetoone, differentiable function and its inverse function f^−1 is also differentiable. One can show, using implicit differentiation (do it!), that (f^−1)′(x)=1 / f′(f^−1(x)) Find (f^−1)′(−6) if f(−1)=−6 and

Calculus
f(x) and g(x) are a differentiable function for all reals and h(x) = g[f(2x)]. The table below gives selected values for f(x), g(x), f '(x), and g '(x). Find the value of h '(1). (4 points) x 1 2 3 4 5 6 f(x) 0 3 2 1 2 0 g(x) 1 3 2 6 5 0 f '(x) 3 2 1 4 0 2

calculus
Let f be the function defined by f(x)=2x+3e−5x, and let g be a differentiable function with derivative given by g′(x)=1x+4cos(5x). It is known that limx→∞g(x)=∞. The value of limx→∞f(x)g(x) is

math
Let f be the function defined as: f(x) = (x^2  4)/ (x2) if x≠2 1 if x=2 Which of the following statement(s) about f is true? A. f has limit at x=2 B. f is continuous at x=2 C. f is differentiable at x=2

Calculus
Sketch the graph of a function that is continuous at x=5 but not differentiable at x=5.

Calculus
1. The function is continuous on the interval [10, 20] with some of its values given in the table above. Estimate the average value of the function with a Left Hand Sum Approximation, using the intervals between those given points. x 10 12 15 19 20 f(x)

Calculus AP
f is a differentiable function on the interval [0, 1] and g(x) = f(2x). The table below gives values of f ′(x). What is the value of g ′(0.1)? x 0.1 0.2 0.3 0.4 0.5 f ′(x) 1 2 3 –4 5 The answers are: 1 2 4 cannot be determined I got 1 please let me

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 (x24)*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

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

Derivatives
Determine the interval on which The function is differentiable : f(x) = 3x  5

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..

Calculus Please Check my answers
f is a function that is differentiable for all reals. The value of f ′(x) is given for several values of x in the table below. The table: x 8,3,0,3,8 f'(x)4,2,0,4,5 If f ′(x) is always increasing, which statement about f(x) must be true? f(x)

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) =

Mathmatics
Let f be the function defined by f(x)=2x+3e^−5x, and let g be a differentiable function with derivative given by g′(x)=1/x+4cos(5/x). It is known that limx→∞g(x)=∞. The value of limx→∞f(x)/g(x) is

Calculus
1. Provide an example of a function f that is continuous at a = 2 but not differentiable at a = 2. 2. Provide an example of a function g that is differentiable at a = 3 but does not have a limit at a = 3. Thanks!

Math
The twice–differentiable function f is defined for all real numbers and satisfies the following conditions: f(0)=3 f′(0)=5 f″(0)=7 a)The function g is given by g(x)=e^ax+f(x) for all real numbers, where a is a constant. Find g ′(0) and g ″(0) in

Math
The function f(x)=x^2ax if x is less than or equal to 1 and f(x)=ax+b if x is greater than 1 where a and b are constants. If f is differentiable at x=1 then a+b= A.3 B.2 C.0 D.2

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(x2)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

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,

Calculus
A differentiable function called f(x) achieves its maximum when x=0. Which of the following must then be true? 1. The function p(x) = xf(x) has a critical point when x = 0. 2. The function m(x) = (f(x))^2 has its maximum at x = 0. 3. The function j(x) =

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

Calculus
Suppose that f is a differentiable function with derivative 𝑓'(𝑥) = (𝑥 − 3)(𝑥 + 1)(𝑥 + 5). Determine the intervals of x for which the function of f is increasing and decreasing.

Math
Find the value of b, if any, that will make the function differentiable at x = 0 g(x)= { x+b, x

Calculus
Let f be the function defined by f(x)=2x+3e^(−5x), and let g be a differentiable function with derivative given by g′(x)=1/x+4cos(5x). It is known that limx→∞g(x)=∞. The value of limx→∞f(x)/g(x) is

math
If g is a differentiable function such that g(x) < 0 for all real numbers x and if f'(x)=(x24)g(x), which of the following is true?

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 ≠______________

Math11
Hello, I don't know how to do this, please help. Thank you. 1).Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 5x2 − 3x + 2, [0, 2] Yes, it does not matter if f is continuous or differentiable, every

Caclulus
Suppose f is a onetoone, differentiable function and its inverse function fâˆ’1 is also differentiable. One can show, using implicit differentiation (do it!), that (fâˆ’1)â€²(x)=1/fâ€²(fâˆ’1(x)) If f(4)=5 and fâ€²(4)=2/3, find

Calculus
Consider a differentiable function f having domain all positive real numbers, and for which it is known that f'(x)=(4x)x^3 for x>0. A. Find the xcoordinate of the critical point of f. Determine whether the point is a relative maximum, a relative

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) > 0 for x

Math (Function differentiable)
Determine whether the function is differentiable at x=2 x^2+1 for x2 I did the math for the limits of both equations and they both approach to 4. So that means they are differentiable right?

Math
f(x)=x/e^x Show that f is continuous and differentiable for all real numbers.

calculus
sketch graph of a function f that is differentiable and that satisfies the following

Algebra
1. How many real solutions does the function shown on the graph have? The graph is following the function: y=(x+2)^2 A. No real solutions B. One real solution** My answer C. Two real solutions D. Cannot be determined 2. What is the solution to 3x^2+3x+5=0?

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.

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)=(x24)g(x), which of the following is true?

Math
which points of f(x)=arcsin(sinx) are not differentiable? And what is the range of this function? How could I do this without graphing? I am just afraid that my test, which does not allow calculators, will have some question asking me to find this

Calculus
For the following function, find the values of the constants 𝑎 and 𝑏 for which the function is continuous, but not differentiable. 𝑓(𝑥)={𝑎𝑥+𝑏,𝑥>0 & sin𝑥,𝑥≤0.

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.

math 116
What is the difference between domain and range? The domain of a function is the set of all values for the independent variable (in the following example, that's the x) for which the function is defined. That is, if you have a function such as f(x) = 1/x

Calculus
Here is a graph of the derivative y’ of a continuous, differentiable function. For approximately what values of x between 5 and 5 does the original function y have inflection points. Is it 4 inflection points? paste.pics/fa14942466016d4a8e4a0678cf9d8cbb

Calculus Finals Review sheet!! Explanation needed
Here is a graph of the derivative y' of a continuous, differentiable function. For approximately what values of x between Ã¢Ë†â€™5 and 5 does the original function y have inflection points? Find limit as x approaches 3.5 [[x2]]/x (Remember that

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

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?

Calculus help
f is a function that is differentiable for all reals. The value of f ′(x) is given for several values of x in the table below. x –8 –3 0 3 8 f ′(x) 5 4 0 –2 –4 If f ′(x) is always decreasing, which statement about f(x) must be true?

Calculus
f is a differentiable function on the interval [0, 1] and g(x) = f(2x). The table below gives values of f '(x). What is the value of g '(0.1) x .1 .2 .3 .4 .5 f'(x) 1 2 3 4 5 So I know f(x) would be the integral of f'(x) which you can get with a Riemann

Algebra
The vertex of a parabola is at (2,4), and the xintercepts are at 6 and 2. Determine the domain and range of the function. a. D: all real numbers R: all real numbers b. D: all real numbers R: y ≤ 4 c. D: 6 ≤ x ≤ 2 R: y ≤ 4 d. D: x ≤ 4 R: all

calculus
Suppose f is a onetoone, differentiable function and its inverse function f−1 is also differentiable. One can show, using implicit differentiation (do it!), that f(^−1)′(x)=1/ f′(f^−1(x)) Find (f^−1)′(−4) if f(5)=−4 and f′(5)=2/7.

calculus
a) Obtain all solutions of the equation z^3 +1 = 0 b) Let z = x + iy. Obtain the real and imaginary parts of the function f(z) = 1/1+z c) Let f(x + iy) = x^2  y^2 + iv( x,y). Determine a function v such that f is differentiable in the whole complex plane.

Calculus
Use the graph of f(x)=x^2/(x^24) to determine on which of the following intervals Rolle’s Theorem applies. A. [0, 3] B. [3, 3] C. [3/2, 3/2] D. [2, 2] E. none of these I know what the Rolle's Theorem is but I'm unsure on how you know if the function

Calculus
Piecewise function problem. Let f(x)={ax^2+1/3, x is greater than or equal to 1; bx10/3, x

calculus
If g is a differentiable function such that g(x) is less than 0 for all real numbers x and if f'(x)=(x24)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

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?

calculus
Determine whether y is differentiable at x=0 . If it is differentiable, find the derivative at x=0 . y = {x if x0} y' = ( 1 if x0) Yes , it is differentiable at 0. Is the derivative at x=0, 1?

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

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

Math
Is the step function differentiable in its domain? I answered it and said that the step function is not differentiable in its domain because it is not continuous. For the a function to be differentiable it would need to have a value and a limit. However,

Calculus
Let f be a function such that f(−6)=−6, f(6)=6, f is differentiable for all real values of x and −1≤f'x≤1 for all real values of x. Prove that f(x)=x for all −6≤x≤6 I tried applying the mean value theorem here but I'm not sure where to

Maths
Let f be a function such that f(−6)=−6, f(6)=6, f is differentiable for all real values of x and −1≤f'x≤1 for all real values of x. Prove that f(x)=x for all −6≤x≤6 I tried applying the mean value theorem here but I'm not sure where to

MathCalculus
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

maths
prove that the following function is differentiable at x=0 using first principles: f(x)= e^x when x0 or x=0 also is f(x) differntiable for all real x?

mean value theorem
Show that the function f(x)=1x, [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

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

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

General Calculus Question
On a graph what ways can it not be differentiable? I know at cusps it's not differentiable but are there other instances where it is not differentiable?

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)

AP Calculus
Let f be a differentiable function with f(3)= 1 and f'(−3)= 1 and f'(3)= 5 Let the function g(x)=3[f(x)]^2 Write the equation of the line tangent to the graph of gg at the point where x= 3

calculus
Consider the function f(x) = 33 x^{2/3} on the interval [ 1 , 1 ]. Which of the three hypotheses of Rolle's Theorem fails for this function on the inverval? (a) f(x) is continuous on [1,1]. (b) f(x) is differentiable on (1,1). (c) f(1)=f(1). Answer:(

math
Suppose that a

math
Each of the following statements is false. Provide why the statement is false. 1) Every function that is continuous at x=a is differentiable at x=a. 2) The tangent line to y=f(x) when x=x0 is given by y=fprime(x0)x+f(x0). 3) The linerization of a function

factoring
can this equation be factored further? y= x^4+2x^3+4x^2+8x+16 Not in the real number system. If you plot the function, you will see the minimum is at x=1.1 (approx) and y is positive. At no x does the function equal zero, so there are no real roots, which

calculus (hint?)
f(x) is a twice differentiable function such that f(2x)=f(x+5)+(x−5)^2 What is f''(x)?

calc
x^2 + √(x+y) + y^2 = 0; y is a differentiable function of x

Math steve? reiny?
1. Let f(x)=x^5 + 2x^3 + x  1 Find f^1(3) and (f^1)'(3)? I have zero idea how to find the inverse of this function at a point 3, and how to take derivative of an inverse. 2.Let f(x)=cosx + 3x Show that f(x) is a differentiable inverse and find f^1(1)

Calc 1
If a function is continuous, then it is differentiable.

computer science
Can you find the reason that the following pseudocode function does not return the value indicated in the comments? // The calcDiscountPrice function accepts an item’s price and // the discount percentage as arguments. It use those // values to calculate

Maths
If f(x)= max{x2,1,x2} Tell this function is differentiable and continuous at (1,1)????

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)

Algebra
f(x) is a function differentiable at x=1 and fŒ(1)=1/8. What is the value of f(x)f(1) f'(x) denotes the derivative of f(x)

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

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?

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

Math
Find the value of b, if any, that will make the function differentiable at x = 0 g(x)= { x+b, x

Math
Find the value of b, if any, that will make the function differentiable at x = 0 g(x)= { x+b, x

calculus
In the following problem, suppose f(x) is continuous (and differentiable) function on the interval (0,1). Suppose also that for 0 < x>please show steps

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

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

Calculus
Prove that there is no function F that is differentiable everywhere and also satisfies the equation F( x^2+ sin(x) ) = x

calculus
F. (7) (2 puntos posibles) Let f(x)={tanxax+bπ/4

Calculus
Prove that there is no function F that is differentiable everywhere and also satisfies the equation F(x^2+sin(x))=x.

Math
Find d^2y/dx^2 at point P(2,1) if y is a differentiable function of x satisfying the equation: x^3+2y^3=5xy

Calculus help
f(x) and g(x) are a differentiable function for all reals and h(x) = g[f(5x)]. The table below gives selected values for f(x), g(x), f '(x), and g '(x). Find the value of h'(1). x 1 2 3 4 5 6 f(x) 0 3 2 1 2 0 g(x) 1 3 2 6 5 0 f '(x) 3 2 1 4 0 2 g '(x) 1 5

Math
True or false. Let f(x) be a differentiable function, such that f(0)=−3 and f(3)=−3. Then there exists a c with 0≤c≤3 such that the tangent line to y=f(x) is horizontal at x=c

calculus
sketch graph of a function f that is differentiable and that satisfies the following conditions:(1)f'(x)>0, when x

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

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!

Calculus
f(x) and g(x) are a differentiable function for all reals and h(x) = g[f(3x)]. The table below gives selected values for f(x), g(x), f '(x), and g '(x). Find the value of h '(1) Numerical answers expected! x 1 2 3 4 5 6 f(x) 0 3 2 1 2 0 g(x) 1 3 2 6 5 0