Exam 6: Applications of Differentiation

The formula for the power output of battery is where V is the electromotive force in volts, R is the resistance, and I is the current. Find the current (measured in amperes) that corresponds to a maximum value of P in a battery for which volts and ohm. Assume that a 20-ampere fuse bounds the output in the interval . Round your answer to two decimal places.

Match the function with one of the following graphs.

Sketch the graph of the function and locate the absolute extrema of the function on the interval .

Suppose the annual sales S of a new product is given by where t is time in years. Find the exact time when the annual sales are increasing at the greatest rate. Round your answer to three decimal places.

The height of an object t seconds after it is dropped from a height of 700 meters is Find the time during the first 9 seconds of fall at which the instantaneous velocity equals the average velocity.

Determine whether Rolle's Theorem can be applied to the function on the closed interval . If Rolle's Theorem can be applied, find all numbers c in the open interval such that .

Use a computer algebra system to graph the function and determine all absolute extrema on the interval .

Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 100 square meters.

On a given day, the flow rate F (cars per hour) on a congested roadway is given by where v is the speed of the traffic in miles per hour. What speed will maximize the flow rate on the road? Round your answer to the nearest mile per hour.

Determine whether Rolle's Theorem can be applied to on the closed interval If Rolle's Theorem can be applied, find all values of c in the open interval such that

The graph of a function f is is shown below. Sketch the graph of the derivative .

Sketch the graph of the relation using any extrema, intercepts, symmetry, and asymptotes.

Find the points of inflection and discuss the concavity of the function .

The graph shows the temperature T, in degrees Fahrenheit, of molten glass t seconds after it is removed from a kiln. Find

Find all relative extrema of the function . Use the Second Derivative Test where applicable.

Find all relative extrema of the function Use the Second Derivative Test where applicable.

Sketch the graph of the function using any extrema, intercepts, symmetry, and asymptotes.

Find two positive numbers such that the sum of the first and twice the second is 96 and whose product is a maximum.

Find the point on the graph of the function that is closest to the point .

Find the value of the derivative (if it exists) of the function at the extremum point (0,9).