Calculus

Step 1: First Derivative for Extrema.
To find the local maxima and minima, we first find the first derivative of the function:

Step 2: Set the first derivative to zero.
To find critical points, we set : Dividing through by 6: Factoring the quadratic equation:

Step 3: Solve for critical points.
From the equation, we find the critical points and .

Step 4: Second Derivative Test.
Now, we take the second derivative to classify the critical points: Substitute and : - For , , which indicates a local maximum. - For , , which indicates a local minimum.

Final Answer: