Exam 3: Applications of Differentiation

A baseball team plays in a stadium that holds 56,000 spectators. With ticket prices at $9, the average attendance had been 32,000. When ticket prices were lowered to $8, the average attendance rose to 36,000. How should ticket prices be set to maximize revenue? Assume the demand function is linear.

What is the minimum vertical distance between the parabolas ?

Approximate the zero of in to within 0.00001.

For what values of a and b is (2, 2.5) is an inflection point of the curve ? What additional inflection points does the curve have?

Given . (a) Find the intervals on which f is increasing or decreasing. (b) Find the relative maxima and relative minima of F.

Find the critical number(s), if any of the function

The function satisfies the hypotheses of the Mean Value Theorem on the interval . Find all values of c that satisfy the conclusion of the theorem.

A piece of wire m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut for the square so that the total area enclosed is a minimum? Round your answer to the nearest hundredth.

Find the absolute maximum value of .

Sketch the graph of the function on using the curve-sketching guidelines.

Use the Second Derivative Test to find the relative extrema, if any, of the function .

Find the most general antiderivative of the function.

Find the limit.

Given . (a) Find the intervals on which f is increasing or decreasing. (b) Find the relative maxima and relative minima of f.

A manufacturer has been selling 1,200 television sets a week at $400 each. A market survey indicates that for each $30 rebate offered to the buyer, the number of sets sold will increase by 60 per week. Find the demand function.

How many points of inflection are on the graph of the function?

Find the absolute minimum value(s) of on the interval [0, 6].

To what constant deceleration would a car moving along a straight road be subjected if the car were brought to rest from a speed of 86 ft/sec in 7 sec? What would the stopping distance be?

Find the limit.

Find two numbers whose difference is 170 and whose product is a minimum.