Question

$f\left(x\right)=4+5x^2+6x^4$ has

• A. only one minimum
• B. neither maximum nor minimum
• C. only one maximum
• D. two local minimum

Answer 1

The correct option is A only one minimum

$f\left(x\right)=4+5x^2+6x^4$
$\Rightarrow f^{\prime }\left(x\right)=10x+24x^3=2x(5+12x^2)$
From $f^{\prime }\left(x\right)=0\Rightarrow x=0$


Since, sign of $f^{\prime }\left(x\right)$ changes from negative to positive as $x$ crosses $0$ from left to right, therefore $x=0$ is a point of local minima.