Q36

MSQ2 marks

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined as follows:

f(x)=\left(\frac{|x|}{2}-x\right)\left(x-\frac{|x|}{2}\right)

Which of the following statements is/are true?

(A)

$f$ has a local maximum

(B)

$f$ has a local minimum

(C)

$f^{\prime}$ is continuous over $\mathbb{R}$

(D)

$f^{\prime}$ is not differentiable over $\mathbb{R}$

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