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

b. x=2

Table showing values of x, f(x), and f prime(x) at points 0 to 4, used to find the slope of the inverse function at x=2.

Accepted Answer

Welcome back, everyone. Evaluate the slope of F inverse of X at X equals 1 using the table given below. A 1/2, B6, C 112, and D 16th. For this problem, let's remember that the slope is basically the derivative at a specific point. So we want to find the derivative of F inverse. And let's state the general property, the derivative of F inverse. Of X is going to be equal to 1 divided by the derivative of F at a point F inverse of X. So now in this case, we know that X is equal to 1. Meaning we can use this formula to show that F inverse. At one. Derivev So let's clean it up and let's write it properly. We can just say F inverse. Derivative at. 0.1. Is equal to one divided by. F derivative at F inverse. At 1, right? In other words, we're just replacing X with 1 because that's the point of interest. So now, this is exactly what we want to identify. We want to evaluate F inverse derivative, 1 X is equal to 1, and we can use the right hand side of this expression. So, let's begin with what's given in recies. We want to find F inverse at 1. And if we use the table. Based on the table we are given. That F of 2 is equal to 1, right? Let's remember that according to the properties of inverse functions, we basically flip the domain and range. So if F of 2 is equal to 1, F inverts at 1 is going to be equal to 2, we are flipping X and Y. So F inverse of 1 is equal to 2, based on the fact that F of 2 is equal to 1, right? This is how we can identify the value. Of the inverse function at X equals 1. We want to find when F of X is equal to 1 itself, and we want to extract the X coordinate, which in this case is 2. So, we have now shown that F inverse derivative, when X is equal to 1. is equal to 1 divided by f derivative at 2. Because F invert set 1 is equal to 2. And then we can use the table F derivative at X equals 2 is equal to 12 based on the table. So our final answer is 1/12, which corresponds to the answer choice C. 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) atb. x=2

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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
b. x=2