Question #$1$

Given $f(x)=4-x^2$ for $f(x)0$ : A rectangle is constructed with two vertices on the curve $f(x)$ and two on the $x-$axis as shown in the diagram. What is the maximum perimeter of the rectangle?

Question #$2$

A poster is to contain $100$ square inches of picture surrounded by a $4-$ inch margin at the top and bottom and a $2-$ inch margin on each side.

a$.$ Make a sketch

b$.$ Find the overall dimensions that will minimize the total area of the poster.

Question #$3$

A $10$ ft plank is leaning against a wall. If at a certain instant the bottom of the plank is $2$ ft from the wall and is being pushed toward the wall at a rate of $6i\frac{n}{s},$ how fast is the acute angle that the plank makes with the ground increasing? $($Hint: convert $6i\frac{n}{s}$ to feet$)$