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
easyFind the local maximum and minimum values of f(x) = x^3 - 3x + 2.
Example 2
hardA farmer has 200 m of fencing to enclose a rectangular field. What dimensions maximize the enclosed area?
Example 3
easyFind the critical points of f(x) = 2x^3 - 9x^2 + 12x - 4 and classify them.
Example 4
mediumFind the absolute maximum and minimum of f(x) = x^3 - 6x^2 + 9x + 1 on [0, 4].