Locating critical points Find the critical points of the following functions. Assume a is a nonzero constant.


ƒ(x) = 3x³ + 3x² / 2 - 2x

Verified step by step guidance

1. Start by finding the derivative of the function ƒ(x) = 3x³ + (3/2)x² - 2x. This will help identify where the function's slope is zero or undefined.
2. Set the derivative equal to zero to find the critical points. This means solving the equation f'(x) = 0.
3. Factor the derivative if possible to simplify the equation and make it easier to solve for x.
4. Solve for the values of x that satisfy the equation from the previous step. These x-values are the critical points.
5. Verify if the critical points are indeed critical by checking if the derivative is undefined at any of these points.