Question

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

Answer 1

$y=2x^2+x+2$

$\frac{dy}{dx}=4x+1=0\Rightarrow x=-\frac{1}{4}$

$\frac{d^{2}y}{d{x}^2}=4>0\left(always\right)$

The function increases continously from $[-\frac{1}{4},\infty ]$ and decreases continously from $[-\infty ,-\frac{1}{4}]$ and the minimum at $x=-\frac{1}{4}$