Question

Minimum of the real valued function $f\left(x\right)=(x-1{)}^{2/3}$ occurs at $x$ equal to

• A. $-\infty$
• B. $0$
• C. $1$
• D. $\infty$

Answer 1

The correct option is C $1$

$f\left(x\right)=(x-1{)}^{2/3}$
$f^{\prime }\left(x\right)=\frac{2}{3}(x-1{)}^{-1/3}$





So, $f^{\prime }\left(x\right)=0\Rightarrow x=1$ is a critical point.
$f^{\prime }\left(1^{-}\right)<0$
and $f^{\prime }\left(1^{+}\right)>0$
$\Rightarrow f\left(x\right)$ has minima at $x=1$.