Chapter 3.2, Problem 43E

To determine

For what value of $a$ from (A) $a=1$ (B) $a=-1$ (C) $a=2$ (D) $a=-2$ (E) $a=0$ , $f\text{'}\left(a\right)\ne \text{NDER}\left(f\left(x\right),x,a\right)$ .

Answer to Problem 43E

The correct option is (A).

Explanation of Solution

Given information:

The function: $f\left(x\right)=\sqrt[3]{x-1}$

The given options

(A) $a=1$ (B) $a=-1$ (C) $a=2$ (D) $a=-2$ (E) $a=0$ .

The given function is $f\left(x\right)=\sqrt[3]{x-1}$ .

Draw the graph of $f\left(x\right)$ .

  

Since, $f\left(x\right)$ has a vertical tangent at $x=1$ .

Thus, $f\left(x\right)$ is not differentiable at $x=1$ .

At $a=1$ , $f\text{'}\left(a\right)\ne \text{NDER}\left(f\left(x\right),x,a\right)$

Hence, the correct option is (A).