Find the local maximum and local minimum points of the function .
Given that the function is differentiable, , and , then has a local maximum value at .
Likewise, if and , then has a local minimum value at .
First, find the derivative of the function as follows:
Now substitute 0 for in the equation and solve for .
Next, find the second derivative of the function .
Now substitute 0 for in the equation to find .
Since , the function has a local minimum value at .
Now substitute for in the equation to find .
Thus, since , the function also has a local minimum value at .