Derivatives of inverse functions from a table Use the followin...

Question

Derivatives of inverse functions from a table Use the following tables to determine the indicated derivatives or state that the derivative cannot be determined.

c. (f^-1)'(1)

Accepted Answer

Welcome back, everyone. Evaluate the following derivative using the table given below. We want to evaluate H inverse derivative at -2. We're given the table and 4 answer choices A says 1/5, B5, C 1/2, and D says cannot be determined. So essentially, let's remember one of the properties of derivatives. Let's suppose that we want to take the derivative of the inverse function H inverse. At point A. We can recall the identity. It says that it is going to be equal to 1 divided by the derivative of h at a point of H inverse at point A. So we're going to use this property. And now in this case our A, the point of interest, is going to be equal to -2. So we can rewrite this as h in verse. The derivative at 0.2 is equal to 1 divided by the derivative of h at point h inverse. At 0.-2. Now our table gives us the values of X, H of X, and H of X, right? So essentially what we want to do is understand what type of a value we have inside of prics. H inverts at -2 can be evaluated as follows in terms of h. This is the X value. Or which The original parent function in this case H of X, not the inverse, right? Is equal 22. Because we are essentially swapping the domain and range when it comes to the comparison of the parent function and its inverse. So essentially we want to identify the X value for which H of X is equal to -2. Now let's look at the table. We have H of X in the second row, right, and we want to identify the value of -2. We have 8, we have 3. Followed by 49, and 12. So in the table we are not given h of X equals -2, right? So we don't know what X is because we don't know what X is we cannot proceed with a given equation. So essentially we can conclude that it cannot be determined and the correct answer corresponds to the answer choice d. Thank you for watching.

Derivatives of inverse functions from a table Use the following tables to determine the indicated derivatives or state that the derivative cannot be determined. <IMAGE>
c. (f^-1)'(1)

Key Concepts

Inverse Functions

Derivative of Inverse Functions

Using Tables for Derivatives

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