5.6 Solving Optimization Problems Homework Apr 2026

Optimization problems are the “real reason” we learn calculus: to find the best (maximum profit, minimum cost, largest area, shortest time) given some constraint.

$y = 200 - 2(50) = 100$ ft.

$A'(x) = 200 - 4x$.

Welcome to the homework section of Section 5.6. If you’ve made it here, you’ve survived derivatives, critical points, and the first and second derivative tests. Now, it’s time to apply all of that to the real world—or at least to the world of word problems. 5.6 Solving Optimization Problems Homework

$A''(x) = -4 < 0$, so concave down → maximum. Optimization problems are the “real reason” we learn

$200 - 4x = 0 \implies x = 50$ ft.