Exam 4: Applications of the Derivative

Suppose that the body temperature 30 minutes after receiving x mg of a drug is given by for . The absolute value of the derivative, , is defined as the sensitivity of the body to the drug dosage. Find the dosage that maximizes sensitivity.

Use a linear approximation to estimate Note that 16.9 is near 16 which is

Find the volume of the largest box with no top that can be made from a piece of cardboard 30 inches square by cutting equal squares from the corners and turning up the sides.

Find the error in the following incorrect calculation.

Find the x-coordinates of all extrema and sketch the graph of showing global and local behavior. Round answer to nearest thousandth.

Given , on the interval , determine the critical number(s).

Find the limit.

A handbill is to contain 200 square inches of printed material, with 4-inch margins at the top and bottom and 2-inch margins on each side. What dimensions for the handbill would use the least amount of paper?

Suppose that at the price dollars the demand for a product is elastic. If the price is decreased, what will happen to revenue?

Determine the intervals where is concave up and concave down.

Suppose that a population grows according to the logistics equation . Find the population at which the population growth rate is a maximum.

Find the limit.

Determine all significant features and sketch a graph.

The power required for a particular bird to fly at a speed is proportional to Find to minimize the power.

Find the x-coordinates of all extrema and sketch the graph of showing global and local behavior.

A rectangle has its two bottom corners lying on the x-axis and the two top corners on the parabola , where . If the area of the rectangle is to be maximized, then what are its dimensions?

Find all critical numbers.

Determine all significant features and sketch a graph.

Oil spills out of a tanker at the rate of 125 gallons per minute. The oil spreads in a circle with a thickness of 1/4 inch. Given that 1 ft³ equals 7.5 gallons, determine the rate at which the radius of the spill is increasing when the radius reaches 50 feet.

Find the elasticity of demand if .