Finding Local Extrema Using the Second-Derivative Test

Hi Ayliz, let's find the local maxima and minima for this cubic function using the second derivative test.

To find local extrema, our first step is to calculate the first derivative and find the critical points.

Using the power rule, the derivative f prime of x is three x squared minus twelve x plus nine.

We set this derivative equal to zero to solve for our critical values.

To make solving easier, let's factor out a three from the entire equation.

Now we factor the quadratic inside the parentheses. We need two numbers that multiply to three and add to negative four.

Setting each factor to zero, we find our critical points at x equals one and x equals three.