Question

Let \[ f(x)= \begin{cases} -150-25x, & -10\le x\le -5,[2mm] x|x|, & -5\le x\le 5,[2mm] 150-25x, & 5\le x\le 10. \end{cases} \] Which of the following is correct?

• A. \(f(x)\) is continuous at all points except at \(x=\pm5\)
• B. \(f(x)\) is differentiable at all points except at \(x=\pm5\)
• C. \(f(x)\) is not differentiable at \(x=0\) since \(|x|\) is not differentiable at \(x=0\)
• D. \(f(x)\) has \(4\) points of discontinuity

Hint:

A piecewise function may be continuous but not differentiable at the joining points. Always check both continuity and equality of the left and right derivatives.

Answer 1

The Correct Option is B