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Chapter 2: Q42E (page 77)

The graph of \(f\) is given. State, with reasons, the numbers at which \(f\) is not differentiable.

Short Answer

Expert verified

The numbers at which \(f\) is not differentiable are \(x = - 1\) and \(x = 2\).

Step by step solution

01

 Step 1: Differentiability of the Function

The function is known to be a differentiable function if and only if it is continuous function and the derivative of that function exists for any point within its domain.

02

Find the numbers at which the function is not differentiable.

The given graph is:

Clearly, at\(x = 2\), the curve shows the inflection that broke differentiability of this function and at \(x = - 1\), the function is discontinuous.

Hence, the numbers at which \(f\) is not differentiable are \(x = - 1\) and \(x = 2\).

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Most popular questions from this chapter

Sketch the graph of the function g for which \(g\left( {\bf{0}} \right) = g\left( {\bf{2}} \right) = g\left( {\bf{4}} \right) = {\bf{0}}\), \(g'\left( {\bf{1}} \right) = g'\left( {\bf{3}} \right) = {\bf{0}}\), \(g'\left( {\bf{0}} \right) = g'\left( {\bf{4}} \right) = {\bf{1}}\), \(g'\left( {\bf{2}} \right) = - {\bf{1}}\), \(\mathop {{\bf{lim}}}\limits_{x \to \infty } g\left( x \right) = \infty \), and \(\mathop {{\bf{lim}}}\limits_{x \to - \infty } g\left( x \right) = - \infty \).

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