Locate 1) the position and nature of the stationary points and 2) the points of inflection of the following curve
y = x^4 - 6x^2 +15
Find $\displaystyle \frac{dy}{dx}$ of the $\displaystyle y$, then put that expression equal to zero, which will give you the x co-ordinates of the points at which the gradient is 0 i.e. stationary points etc.
To classify the inflexion point, find the gradient at the points either side of the place where the gradient is equal, if both results provide gradients with the same sign i.e. +ve or -ve, then it is inflection.
$\displaystyle \frac{dy}{dx} = 4x^3 - 12x$