Question

The function which has neither maximum nor minimum at x =0=0 is

• A. $f\left(x\right)=x^2$
• B. $f\left(x\right)=\cos x$
• C. $f\left(x\right)=x^3-8$
• D. $f\left(x\right)=\cos$ hx

Answer 1

The correct option is C $f\left(x\right)=x^3-8$

(A) If $f\left(x\right)=x^2$
$f^{\prime }\left(x\right)=2x$ so $f\left(x\right)$ have minima at $x=0$
(B) $f\left(x\right)=cosx$
$f^{\prime }\left(x\right)=-sinx$ so $f\left(x\right)$ have maxima at $x=0$
(C) $f\left(x\right)=x^3-8$
$f^{\prime }\left(x\right)=3x^2$ so $f\left(x\right)$ is neither maxima nor minima