Exam 4: Using the Derivative

The following three equations are graphed in the figure. Which graph corresponds to equation C? A. B. C.

Raising the average price of an entree at a restaurant from $13 to $15 reduces the number of customers per day from 225 to 175. A. What is the elasticity of demand to two decimal places for entrees at a price of $13? B. Would raising the price from $13 to $15 increase or decrease the profit?

Given . Which of the following are critical points of f?

The average cost per item to produce q items is given by for q>0. What is the total cost, C, of producing q goods?

You sell hot dogs at a baseball game for $3.25 each. You have 100 hot dogs to sell at an average cost to you of $2.00 each. The marginal cost at q=100 is $1.95. Assume you can always sell out of hot dogs. Will increasing the number of hotdogs you have to sell increase or decrease your profit?

The demand curve for a product is . A. Find the elasticity of demand (to three decimal places) at a price of p=5. B. Is demand elastic or inelastic at this price?

What quantity of gadgets should be produced to maximize profit if they sell for $500 per unit and the total cost (in dollars) of producing x units is given by ? What is that profit?

The total revenue and cost curves for a product are shown in the first figure. Does the second figure accurately show the corresponding marginal cost and marginal revenue functions?

A disease is released into a town. The number of people infected each day is modeled by the equation . Estimate when Estimate the value of n at this time.

The rabbit population, P, in a wilderness area is approximated by the function , where t is the number of weeks since the rabbits were introduced into the area. A. How many rabbits were initially introduced into the area (to the nearest rabbit)? B. How many rabbits were in the area after 5 weeks (to the nearest rabbit)? C. What is the carrying capacity of rabbits in the area?

Classify the following graph as a probable logistic, polynomial, or surge function

The following table gives the number of students who have joined a new school club t days after it was formed. A. Estimate the value of t where concavity changes in this function. B. Use your answer from part (a) to estimate the maximum membership in the club.

For and , find the value(s) of x for which A has a local minimum. B has a local maximum. C. has a global minimum. D. has a global maximum. List the value(s) from smallest to largest, separated by commas.

You sell hot dogs at a baseball game for $2.75 each. You have 100 hot dogs to sell at an average cost to you of $1.75 each. The marginal cost at q=100 is $1.90. Assume you can always sell out of hot dogs. Will increasing the number of hot dogs you have to sell increase or decrease the average cost?

If time, t, is in hours and concentration, C, is in ng/ml, the drug concentration curve for a drug is given by . About how many hours does it take for the drug to reach peak concentration? .

The total revenue and cost curves for a product are shown in the following figure. Estimate the production level P that maximizes profit.

The Revenue is given by and the Cost is given by . What value of q will maximize profit? What is the profit at that value? q=________________________, P(q)= ___________________________

The function gives the population of a town (in 1000's of people) at time x where x is the number of years since 1980. The population was a minimum in the year _____.

A water park finds that at an admission price of $20, attendance is 300 per day. For every $1 decrease in price, 50 more people visit the park per day. How many dollars should the park chanrge for admission to maximize revenue (to the nearest dollar)?

The number of plants in a terrarium is given by the function , where c is the number of mg of plant food added to the terrarium. The amount of plant food that produces the highest number of plants is _____ mg (round to the nearest hundredth).