Question

Find the critical points of the following function and test them for their maxima and minima.
$y=x^4-10x^2+9$

Answer 1

$y=x^4-10x^2+9$

$\frac{dy}{dx}=4x^3-20x=0\Rightarrow x=\pm \sqrt{5}$

$\frac{d^{2}y}{d{x}^2}=12x^2-20$

At $x=\pm \sqrt{5},\frac{d^{2}y}{d{x}^2}>0$, Hence y has its minimum at $x=\pm \sqrt{5}$ and increases after that ,i.e no maximums.