AP Calculus AB Fun 4 B Calculate Minimum and Maximum Values in Applied Contexts or Analysis of Functions Questions

Practise optimization questions by defining an objective, using derivatives to locate critical points and checking endpoints and context.

Exam points

define an objective function and identify feasible critical points
justify an absolute minimum or maximum using derivative and endpoint evidence

[Maximum number: 1]

A rectangle has its upper two vertices on the graph of $y=12-\frac{x^{2}}{3}$ and its lower two vertices on the x-axis. What is the maximum possible area of the rectangle?

$216-72 \sqrt{5}$

$32 \sqrt{3}$

144

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AP Calculus AB Fun 4 B Calculate Minimum and Maximum Values in Applied Contexts or Analysis of Functions Questions question 1