Question

$f\left(x\right)=\{\begin{array}{cc}-2x& x<0\\ 3x+5& x\ge 0\end{array}$ Check the existence of max. or min. at x=0.

• A. min.
• B. max.
• C. both min and max
• D. neither min nor max

Answer 1

Answer: (D)

neither min nor max

$\underset{x\to 0^{-}}{lim}f\left(x\right)$

$=-2\left(0\right)$
$=0$.

$\underset{x\to 0^{+}}{lim}f\left(x\right)$

$=3\left(0\right)+5$
$=5$
Hence

$LHL\ne RHL$ at $x=0$.

Therefore $f\left(x\right)$ is discontinuous at $x=0$

Thus it is not differentiable at $x=0$