Question

If function $f\left(x\right)=\{\begin{array}{cc}2x,& x\le 0\\ a-\left\{x\right\},& 0<x<1\end{array}$ has a local maximum at $x=0,$ then which of the following can be a possible value of ${}^{\prime }{a}^{\prime }$

• A. $\frac{3}{5}$
• B. $0$
• C. $\frac{2}{5}$
• D. $-\frac{1}{5}$

Answer 1

Answer: (B), (D)

$-\frac{1}{5}$

For maximum at $x=0:$
Plotting the graph of $f\left(x\right):$

From graph, it is clear that $a\le 0,$ for maximum at $x=0$