# 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)

86,842 results

### 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) passes through the origin ...

### 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, the step function has ...

### 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 ...

### Math (Function differentiable)

Determine whether the function is differentiable at x=2 x^2+1 for x<(or equal to) 2 4x-3 for x>2 I did the math for the limits of both equations and they both approach to 4. So that means they are differentiable right?

### Caclulus

Suppose f is a one-to-one, 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 (fâˆ’1)(5). (f...

### 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) ...

### Math

Suppose the amount of bacteria growing in a perti dish is represented by the function b(t)=50t/t+1 Evaluate the function at t=1,2,5,10,15,20 (a) constract a table of values (b) use the table to sketch a graph.

### econ question

2 questions that im stuck on!!! 1. Suppose a firm has a production function Q = 3(squareroot)N, where N is labour. Suppose the wage is 3, and the price of the output 4. (a) Write the Firm profits (b) Calculate the firm optimal labour choice when the wage is 3. 2. 2. Suppose a ...

### 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...

### 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 ...

### Math

Make a table and graph each quadratic function. Use integers from -3 to 3 for inputs. #4- y= -x2 #5- y=2x squared #6- y= -8x squared #7- y= x squared + 2 Make a table and a graph for each function. Use only positive values for x. #10- y= 10/x #11- y= 8/x Write a quadratic ...

### Calculus

Use the graph of f(x)=x^2/(x^2-4) 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 is continuous 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 g '(x) 1 5 4 3 2 0

### calculus

I am given a table that shows the temperature of the water and the days, which looks like this: t(days) W(t) (in Celcius) 0 20 3 31 6 28 9 24 12 22 15 21 the temperature of the water in a pond is a differentiable function W of time t. The table above shows the water ...

### Math I need help ASAP!

1) Identify the function rule shown in the table. Function Table n - 3, 4, 5, 6 y - 2, 1, 0, -1 a. y = 2 + n b. y = 5n c. y = 5 - n d. not enough information ** 2) What is the values of the function y = -2x - 4 for x = 0,1,2 and 3? a. 0, -6, -8, -10 b. -4, -6, -8, -10 ** c. -4...

### 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?

### Precalculus

The application of one function followed by the application of a second function to the result of the first as in F^-1(f(x)) is called composition of functions. The two functions need not be inverse of each other. In a diagram, the output of one function is f(x) is used as the...

### math

The application of one function followed by the application of a second function to the result of the first as in F^-1(f(x)) is called composition of functions. The two functions need not be inverse of each other. In a diagram, the output of one function is f(x) is used as the...

### 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!

### 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...

### 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...

### 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 function satifies the ...

### 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 information. Also, when are ...

### Calculus

The rate at which water flows into a tank, in gallons per hour, is given by a differentiable function R of time t. The table below gives the rate as measured at various times in an 8-hour time period. t---------0-----2------3-------7----8 (hours) R(t)--1.95---2.5---2.8----4.00...

### 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...

### Math

A function f is defined by the equation f(x)=4x−8. Suppose that the state variables T and Q are related by this function according to the mapping f:Q↦T. Suppose that T=3. Use the equation of the function to find the value of Q.

### 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

### 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

### 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 ...

### 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

### Math Ms. Sue please

6. Use the function rule ƒ(x) = x2 – 5x + 1. Find the output ƒ(–3). (1 point) 7 –5 25 5 7. Suppose you earn $12 each time you mow the lawn. Use function notation to describe the relationship between your total earnings E and the number of times m you mow the lawn. (1 ...

### 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

### 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 ...

### 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.

### Calculus Please Check my answer

The rate at which water flows into a tank, in gallons per hour, is given by a differentiable function R of time t. The table below gives the rate as measured at various times in an 8-hour time period. t---------0-----2------3-------7----8 (hours) R(t)--1.95---2.5---2.8----4.00...

### 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 ≠______________

### 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) = f(x^2) has its maximum ...

### 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...

### 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?

### 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...

### Math Help Please!!!

Use the function rule to complete the table Table= x= -2, -1, 0, 1, 2 y= (figure out y) Function rule= -10x+y=4

### Calculus

Piecewise function problem. Let f(x)={ax^2+1/3, x is greater than or equal to 1; bx-10/3, x<1. If the function is differentiable, find the sum of a+b.

### Calculus

Suppose that f(x) and k(x) are differentiable everywhere and that f(3) = 5, f'(3) = 7, k(3) = 6, and k'(3) = 9. Find an equation of a tangent line to 3(f(x))^2 at x = 3. So the derivative of 3(f(x))^2 is 6f(x)*f'(x), and 6f(3)*f'(3) is 210. But for the tangent line, should I ...

### Math

use the table below to answer the question that follows. n 2 4 6 <--- this is the table m -8 -16 -24 Which function would help you find the values in the table A.m = -2n B.m = n-2 C.m = n-4 D.m = -4n*** My Answer Is D am i right

### physics

How am I supposed to answer this question on the lab write-up? I have the date, but I don't know the formula or process to use. Thanks. Organizing Data: Using your estimate of the threshold frequency from your first data table and your measured value of ft for sodium from your...

### 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 ...

### calculus

suppose that f(x) = x^3 x<=1 ax+b x>1 is differentiable at x=1 then a=?, b=?

### Math

Suppose f(x)= |x^(2)+2x−63|. Where is f(x) not differentiable?

### economics

suppose Y=100 is fixed,suppose the consumption function is c(Y-T)=20+M(Y-T), where M is constant between 0&1,suppose the investment function is I(r)=30-50r,suppose we leave G&T as un specified constant.drive equilibrium interest rate&predict effect of increase i G on r

### 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

### Math- Calc

Suppose f(x)= |x^(2)+2x−63|. Where is f(x) not differentiable?

### 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- 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) and (f^-1)'(1). ...

### Math

1.Mia charges $2.25 per hour when she babysits, plus $5.00 for transportation expenses.Which function rule represents the amount y mia charges to babysit for x hours? A)Y = 2.25x + 5.00*** B)X = 5.00y + 2.25 C)Y = 5.00x + 2.25 D)Y = 7.25x 2.(So this one is my updated answer, ...

### 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) ]

### 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) =

### Math

Find the value of b, if any, that will make the function differentiable at x = 0 g(x)= { x+b, x<0 cos(x), x≥0 can you help, I got 0 but I don't know if that will make the function differential at x=0.

### Math

Find the value of b, if any, that will make the function differentiable at x = 0 g(x)= { x+b, x<0 cos(x), x≥0 can you help, I got 0 but I don't know if that will make the function differential at x=0.

### Math

Find the value of b, if any, that will make the function differentiable at x = 0 g(x)= { x+b, x<0 cos(x), x≥0 can you help, I got 0 but I don't know if that will make the function differential at x=0.

### calc

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

### Calc 1

If a function is continuous, then it is differentiable.

### calc help

t= hours 0 1 3 4 7 8 9 l(t) people 120 156 176 126 150 80 0 concert tickets went on sale at noon (t=0) and were sold out within 9 hours. the number of people waiting in line to purchase tickets at time t is modeled by a twice-differentiable function L for 0< = 0 < = 9. ...

### calc

t= hours 0 1 3 4 7 8 9 l(t) people 120 156 176 126 150 80 0 concert tickets went on sale at noon (t=0) and were sold out within 9 hours. the number of people waiting in line to purchase tickets at time t is modeled by a twice-differentiable function L for 0< = 0 < = 9. ...

### Math

What is an estimate of the solution of the equation 6n+3=2? Use a table ok so I know the answer is -1/6 but its asking to use a table? does anyone know what kind of table you use for this and how I'd use it? thank you soo much

### Math

What is an estimate of the solution of the equation 6n+3=2? Use a table. ok so I know the answer is -1/6 but its asking to use a table? does anyone know what kind of table you use for this and how I'd use it? thank you soo much

### Statistics:Z and T Statistics: Confidence Interva

Z and T Statistics: Confidence Intervals and Significance Tests: A friend who hears that you are taking a statistics course asks for help with a specific chemistry lab report. She has made four independent measurements of the specific gravity of a compound. The results are : 4...

### math help ASAP

Rico made a function table to illustrate the rate he charges for mowing lawns. Complete the table. Then write a function rule for the function. (1 point) ( ) = blank Hours (h) 1 2 3 4 5 Earnings (E) ( ) ( ) ( ) $22.00 $27.50 a. $5.75, $11.50, $17.25; E = 5.75h b. $6.00, $12.00...

### 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. Express f as a ...

### 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

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

### 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)

### 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)

### math

Sinx square algerbra of differentiable function

### Math help! Hurry Please~

1. Scientists estimate the rate of the wildebeest running at full speed to be 66 feet per second. Write a function rule to describe the relationship between the time, t, and the distance ,d, a wildebeest travels when running at full speed.(1 point) a. t = 66d b. 66 = d • t c...

### Calculus

Consider a differentiable function f having domain all positive real numbers, and for which it is known that f'(x)=(4-x)x^-3 for x>0. A. Find the x-coordinate of the critical point of f. Determine whether the point is a relative maximum, a relative minimum, or neither for ...

### 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.

### Math

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

### calculus

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

### 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 (hint?)

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

### 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 ...

### Math

Explain in a variety of ways how you can distinguish the exponential function f(x)=2^x from the quadratic function f(x)=x^2 and linear function f(x)=2x. (Hint: Compare the rate of change using finite differences in table of values; identify a constant ratio in the table of ...

### 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 ...

### algebra

mang pedring wanted to construct a square table such that the length of its side is 30 cm longer than its height. 1. How does the illustration look like? illustrate. 2. How would you represent the height of the table? How about the length of its side? 3. What expression ...

### math

The wave heights h in the open sea depend on the speed v of the wind and the length of time t that the wind has been blowing at that speed. Values of the function h = f(v, t) are recorded in feet in the following table. the values that you need on the table are.. 20hr/30 knots...

### calculus

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

### 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

### 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

Suppose that the number of bacteria in a plate of food is given by N(T)= 10T^2 - 40T + 200, -1<=T<=20 where T is the temperature of the food in degrees Celsius. Suppose that the temperature of the food when it is left out on a picnic table is given by T(t)= 4t + 10, 0<...

### calculus

Suppose that the number of bacteria in a plate of food is given by N(T)= 10T^2 - 40T + 200, -1<=T<=20 where T is the temperature of the food in degrees Celsius. Suppose that the temperature of the food when it is left out on a picnic table is given by T(t)= 4t + 10, 0<...

### calculus

Rolle's theorem cannot be applied to the function f(x) = x1/3 on the interval [–1, 1] because Answer Choices: f is not differentiable on the interval [–1, 1] f(–1) ≠ f(1) f is not differentiable on the interval [–1, 1] and f(–1) ≠ f(1) Rolle's theorem can be ...

### compemtary math

. To determine the compound amount of an investment of $10,000 with an interest rate of 6% compounded monthly after 4 years requires you to use a table factor that goes beyond the Compound Interest Table. Calculate the new table factor for this investment. Now, using the new ...

### Math

Use the function tables to solve the problems. Table :2 Input ( Number of Pies Sold). Output( cost) 1. $ 12.65 2 3 $ 37.95 4 What is the rule for Table 2 ? What are the missing output entries in Table 2? 2/ following the same rule set in Table 2 , what would the output number ...

### 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 ...

### Math

complete the function table below for the function F(x) =x2=2 . the numbers in the second row of the completed table make an arithmetic sequence ?.

### Math

Find the missing number that completes the table of values what's the Function Objective a function table Example:y= X+2

### algebra

does the data in the table represent a linear function? if so, wirte a rule for the function. (below is what the table looks like) x | -2| -1| 0 | 1| 2| y | -7| 1| 8 | 17| 25| answer choices yes; y = 8x +9 yes; y = 8x + 8 no yes; y = 1/8x + 8

### math

the table below shows some values for the function f. if f is a linear function, what is the value of a+b? table: X | f(x) 0 | a 1 | 12 2 | b

### 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?