Question

Consider function $f\left(x\right)=(x^2-4{)}^2$ where $x$ is a real number. Then the function has

• A. only one minimum
• B. only two minimum
• C. three minimum
• D. three maximum

Answer 1

The correct option is B only two minimum

$f\left(x\right)=(x^2-4{)}^2$
$f^{\prime }\left(x\right)=2(x^2-4).2x$
For maxima or minima. $f^{\prime }\left(x\right)=0$
$\Rightarrow x=0,-2,2$
$f^{\prime \prime }\left(x\right)=4[3x^2-4]$
$f^{\prime \prime }\left(0\right)=-16<0\Rightarrow$ maximum
$f^{\prime \prime }(-2)=f^{\prime \prime }\left(2\right)=32>0\Rightarrow$ minimum