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Chapter 2: Q. 13 (page 184)

Sketch secant lines on a graph of f(x)=|x|, and use them to argue that the absolute value function is not differentiable at x=0.

Short Answer

Expert verified

The secant lines on a graph are as follows

Step by step solution

01

Step 1. Given information

We have to sketch the secant on a graph of fx=xand by using them, tell that function is not differentiable atx=0.

02

Step 2. Draw the graph for the function

fx=xcan be written as

fx=x,ifx鈮�0-x,ifx<0

So, the graph of the function is

03

Step 3. Draw secant lines and prove graph is not differentiable at x=0

The secant lines are

From secant lines it is observed that at x=0, the slope of the tangent lines approaches to -1from left and 1from right. Therefore, the function is not differentiable atx=0.

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