# Calculus

Given f(x)=−2x^3 -3x + 1, the value of the derivative of the inverse function, f^−1(x) at x=−21 is (f^1)′(−21)= ?

please explain how to solve this

1. 👍 0
2. 👎 0
3. 👁 237
1. Since f(2) = -21,
f^-1(-21) = 2
f'(x) = -6x^2-3

(f^-1)'(-21) = 1/f'(f^-1(-21)) = 1/f'(2) = -1/27

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Functions - math

The function f is such that f(x) = 2x + 3 for x ≥ 0. The function g is such that g(x)= ax^2 + b for x ≤ q, where a, b and q are constants. The function fg is such that fg(x)= 6x^2 − 21 for x ≤ q. i)Find the values of a

use an inverse trig function to write theta as a function of x (There is a right triangle drawn. The hypotenuse is 2. Theta is the angle between the base and the hypotenuse. The base/adjacent side of theta is labeled(x + 1) The

3. ### Calculus Help

The formula C =5/9(F − 32), where F ≥ −459.67, expresses the Celsius temperature C as a function of the Fahrenheit temperature F. Find a formula for the inverse function. What is the domain of the inverse function? (Enter

4. ### Trigonometry

Having trouble with true/false questions in Trigonometry. They read as follows - True or False: For a trigonometric function, y=f(x), then x=F^-1(y). Explain your answer. True or False: For a one to one function, y=f(x), then

1. ### Calculus (Please check my work!)

Suppose that y = f(x) = x^2 - 4x + 4. Then on any interval where the inverse function y = f-1(x) exists, thederivative of y = f-1(x) with respect to x is: (Hint: x^2 - 4x + 4 can be factored and rewritten as "something" squared.)

2. ### Algebra

Myra uses an inverse variation function to model the data for the ordered pairs below. (2, 30), (3, 20), (4, 15), (5, 12), (6, 10) Which statement best explains whether an inverse variation function is the best model for the data?

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

4. ### 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

1. ### calculus

1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))? 2. Find the derivative of f(x) = |x + 2| at the point (1, 3) 3. Find f '(x) for f(x) = -2x3 + 3x2 - x + 15. 4.

2. ### Algebra

I have to find the inverse function of f(x)=3-4x. I got y=3-x/4 for the function. I then have to plug it back into the function and verify that it is the inverse. So I wrote (3-4(3-x))/4. This resulted in (-3+x)/4=x. I tried

3. ### Algebra

Dan works at a hardware store. The employee discount is determined by the formula d = 0.15 (c − 10 ). Use the inverse of this function to find the cost of the item for which Dan received an \$18.00 discount. a. Find the inverse

4. ### Algebra 2

Find the inverse of the following function: f(x) = 3x + 12 I don't think I worked this problem off correctly...I am suppose to find the inverse of the function Is this the correct way to work this problem? y= 3x + 12 x= 3y + 12 3y