Section $3\mathrm{.}5-$ Applied Optimization

Applications

Strategy for Solving Optimization Problems

Dener a picture.

Set up equations.

Get max$/$min eya in terms of cose variable.

Take the derivative.

Answer the question.

Erample f$.$ A cappenter is building a rectangular room with a fixed perimeter of $100$ feet. What are the dimenobos of the largest room that can be built? What is its area?

Erample $2.$ A fence must be built to enclose a rectangular area of $20,000sq.$ ft$.$ Fencing material costs $$3$ per foot for the two sides facing north and south, and $$6$ per foot for the other two sides. Find the cost of the least expensive feerelabel all critical values and inflection poinis find all local mosima and minime as points

$f(x)=x^3-9x^{2}15x10$