# What are the local maxima and minima of f(x) = 4x^3 + 3x^2 - 6x + 1?

Nov 12, 2015

Polynomials are differentiable everywhere , so look for the critical values by simply finding the solutions to $f ' = 0$

#### Explanation:

$f ' = 12 {x}^{2} + 6 x - 6 = 0$

Using algebra to solve this simple quadratic equation:

$x = - 1$ and $x = \frac{1}{2}$

Determine if these are min or max by plugging into the second derivative:

$f ' ' = 24 x + 6$

$f ' ' \left(- 1\right) < 0$, so -1 is a maximum

$f ' ' \left(\frac{1}{2}\right) > 0$, so 1/2 is a minimum

hope that helped