Suppose that the function f and its derivative with respect to...

Question

Suppose that the function f and its derivative with respect to x have the following values at x=0, 1, 2, 3, and 4.

Assuming the inverse function f^(-1) is differentiable, find the slope of f^(-1)(x) at

c. x=3

Table showing values of x, f(x), and f prime of x at points 0 to 4, used to find the slope of the inverse function at x=3.

Accepted Answer

Welcome back, everyone. Evaluate the slope of F inverse of X at X equals A using the table given below. A 17th, B7, C 18, and D 13. For this problem, we want to evaluate the slope of the inverse function of F of X at the given point. So we're going to state the property. The property says that the derivative of F inverse at X is equal to 1. Divided by the derivative of F at a specific point. And that point is F inverse of X. So in this case, we're given that X is equal to 8, meaning The derivative. F inverse. Derivative ant. 8th, we are replacing X with 8th, is going to be equal to 1 divided by. F derivative at F inverse at 8, right? So we didn't see anything yet except from substituting X equals 8th into the equation. And now we want to analyze it because on the left hand side we have our target variable. This is what we want to find. On the right hand side, we have the actual calculation that will be helpful for us. Let's begin with what's inside of brain C's and we want to understand what's F in verse. At 8. How do we find it using the table if the table only gives us X F of X and F of X? Well, F inverse F8 is basically the X value. Or which F of X is equal to 8. So using this property. We are going to use the table and specifically, we want to focus on row number 2, where we have F of X, and we want to locate 8. So F of X is equal to 8th, when X is equal to 3, right? So F of 3 is equal to 8th, meaning F inverse of 8 is equal to 3, because we're flipping X and Y coordinates. So we now know that F inverse at 8 is equal to 3, and we can simplify our expression. F inverse derivative at 8 is 1 divided by F at 3. Once again we can use the table and identify F at 3, which is equal to someone. So the final answer is 17. Which corresponds to the answer to a. Thank you for watching.

Suppose that the function f and its derivative with respect to x have the following values at x=0, 1, 2, 3, and 4.Assuming the inverse function f^(-1) is differentiable, find the slope of f^(-1)(x) atc. x=3

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Suppose that the function f and its derivative with respect to x have the following values at x=0, 1, 2, 3, and 4.
Assuming the inverse function f^(-1) is differentiable, find the slope of f^(-1)(x) at
c. x=3