Question

Find the intervals of increase and decrease of the following function.
$y=2x^3+3x^2-2$

Answer 1

$y=2x^3+3x^2-2$

$\frac{dy}{dx}=6x^3+6x-0$

$\Rightarrow$ for increasing $\frac{dy}{dx}>0$

So $6x^2+6x>0$

$\Rightarrow 6x(x+1)>0$

$xϵ(-1,0)$

and for decreasing

$\frac{dy}{dx}<0$

$\Rightarrow 6x(x+1)<0$

$xϵ(-\infty ,-1)\cup (0,\infty )$.