Question 556891
Take the first derivative and set it equal to zero:


*[tex \LARGE \frac{dy}{dx} = 4x^3 + 18x^2 = 0]


This equals zero at x = 0 and x = -9/2. Now take the second derivative and set it to zero to find possible inflection points:


*[tex \LARGE \frac{d^2y}{dx^2} = 12x^2 + 36x = 0]


x = 0 and x = -3 are the x-coordinates for possible inflection points. Note that you still have to test these points for concavity, as the concavity does not always change when the second derivative equals zero.