For $f(x)=|x|,$ with $\frac{d f}{d x}$ denoting the derivative, the mean value theorem is not

applicable because

(A) $f(x)$ is not continuous at $x=0$

(B) $f(x)=0$ at $x=0$

(C) $\quad \frac{d f}{d x}$ is not defined at $x=0$

(D) $\quad \frac{d f}{d x}=0$ at $x=0$

For $f(x)=|x|,$ with $\frac{d f}{d x}$ denoting the derivative, the mean value theorem is not

applicable because

(A) $f(x)$ is not continuous at $x=0$

(B) $f(x)=0$ at $x=0$

(C) $\quad \frac{d f}{d x}$ is not defined at $x=0$

(D) $\quad \frac{d f}{d x}=0$ at $x=0$

1 Answer

127 votes

(C) $\quad \frac{d f}{d x}$ is not defined at $x=0$

127 votes

127