How do you find critical points and local extrema?

Problem Statement

How do you find critical points and local extrema?

Step-by-Step Explanation

Critical points occur where the derivative is zero or undefined, and they are candidates for local maxima and minima.

1. Identify what the question is asking. In Calculus, this usually means naming the known quantities, the unknown quantity, and the concept that connects them.
2. Write the relevant definition, rule, or relationship before substituting numbers or manipulating symbols.
3. Work one step at a time and keep units, signs, and restrictions visible.
4. Check whether the answer makes sense in the original context.

Final Answer

Critical points occur where the derivative is zero or undefined, and they are candidates for local maxima and minima. The reliable strategy is to start from the definition, apply the correct rule carefully, and then interpret the result in plain language.