# How do you find the exact relative maximum and minimum of the polynomial function of #f(x) = x^3-6x^2+15#?

##### 1 Answer

Mar 13, 2016

Relative maximum:

Relative minimum:

#### Explanation:

Relative maximums and minimums occur whenever the derivative equals 0. Using the power rule, we find the derivative is:

Setting it equal to

To find the exact minimum and maximum, we evaluate these two *critical points*):

Looking at the graph of the function, we can see that there is indeed a local max at

graph{x^3-6x^2+15 [-42.95, 49.5, -19.6, 26.67]}