Exam 12: Applications of the Derivative

A spherical party balloon is being inflated by helium pumped in at a rate 3 cubic feet per minute. How fast is the radius growing at the instant when the radius has reached 1 foot Round your answer to the two decimal places. The volume of a sphere of radius r is $V = \frac { 4 } { 3 } \pi r ^ { 3 }$ .

The weekly sales in Honolulu Red Oranges is given by the following. $q = 950 - 19 p$ Calculate the price that gives a maximum weekly revenue. Round your answer to the nearest cent.

The Chocolate Box Co. is going to make open-topped boxes out of $6 ^ { \prime \prime } \times 14 ^ { \prime \prime }$ rectangles of cardboard by cutting squares out of the corners and folding up the sides. What is the largest volume box it can make this way Round your answer to the nearest whole number.

Maximize $P = x y z$ with $x + y = 9$ and $z + y = 9$ , and $\chi$ , $y$ , and $z > 0$ .

The demand for rubies at Royal Ruby Retailers is given by $q = - \frac { 4 } { 3 } p + 80$ where p is the price RRR charges (in dollars) and q is the number of rubies RRR sells per week. At what price should RRR sell its rubies to maximize its weekly revenue Please enter your answer in dollars without the units.

Calculate $\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }$ . $y = 15 e ^ { - ( x - 5 ) } - x$

The base of a 35-foot ladder is being pulled away from a wall at a rate of 12 feet per second. How fast is the top of the ladder sliding down the wall at the instance when the base of the ladder is 21 feet from the wall ?

Sketch the graph of the function, labeling all relative and absolute extrema and points of inflection, and vertical and horizontal asymptotes. Check your graph using technology. $k ( x ) = \frac { 4 } { 5 } x - ( x - 1 ) ^ { \frac { 4 } { 5 } }$