Question

Let $f\left(x\right)=\{\begin{array}{c}{x}^{3/5}x\le 1\\ -{(x-2)}^{3}x>1\end{array}$
then the number of critical points on the graph of the function is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is C $3$

$f\left(x\right)=\{\begin{array}{c}{x}^{3/5}x\le 1\\ -{(x-2)}^{3}x>1\end{array}$
Critical points will at
At $x=2$, as$f^{{}^{\prime }}\left(x\right)=0$
At $x=0$, $f^{{}^{\prime }}\left(x\right)$ is not defined
At $x=1$, $f^{{}^{\prime }}\left(x\right)$ does not exist , therefore its a critical point.
Thus, there are three critical points.
Hence, option 'C' is correct.