To show:. Give an example of a function which is one-one, but whose inverse fails to be differentiable at a point.
Explanation of Solution
Given information :
The function is differentiable.
Formula used:
To show that a function
Proof:
Assume that the function is
The graph of the function is below:
Graphically the function is one-one as horizontal line cuts the curve at most one.
The derivative is as follow:
which is zero for
Move the positive part to the right.
The graph of the inverse function is
The inverse function will have a jump.
This is because any place where differentiable function has zero slope, the inverse function has infinite slope.
Chapter 3 Solutions
AP CALCULUS TEST PREP-WORKBOOK
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