AP Calculus BC 5.11 Optimization Overview

Model an applied quantity, locate critical points and endpoints, then interpret the absolute maximum or minimum in context.

Exam points

identify the governing calculus relationship in the problem
justify the result with symbolic, graphical or contextual evidence

Covered syllabus points

FUN-4.C—Interpret minimum and maximum values calculated in applied contexts

[Maximum number: 1]

The number of people who have entered a museum on a certain day is modeled by a function f(t), where t is measured in hours since the museum opened that day. The number of people who have left the museum since it opened that same day is modeled by a function g(t). If $f^{\prime}(t)=380\left(1.02^{t}\right)$ and $g^{\prime}(t)=240+240 \sin \left(\frac{\pi(t-4)}{12}\right)$ , at what time t, for $1 \leq t \leq 11$ , is the number of people in the museum at a maximum?

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Table for Question 5.11 Solving Optimization Problems question 1 — AP Calculus BC

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Covered syllabus points

5.11 Solving Optimization Problems question 1