Practice Optimization in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The process of using derivatives to systematically find maximum or minimum values of a function over a domain.

Find where the function hits its peaks (maxima) and valleys (minima) by finding where the slope is zero.

Example 1

easy
Find the local maximum and minimum values of f(x) = x^3 - 3x + 2.

Example 2

hard
A farmer has 200 m of fencing to enclose a rectangular field. What dimensions maximize the enclosed area?

Example 3

easy
Find the critical points of f(x) = 2x^3 - 9x^2 + 12x - 4 and classify them.

Example 4

medium
Find the absolute maximum and minimum of f(x) = x^3 - 6x^2 + 9x + 1 on [0, 4].