Section 14.2 - Applications of Extrema PDF

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Baumgardner's Business Calculus Class...

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Math 1325 Section 14.2 – Applications of Extrema Solving Applied Extrema Problems 1. Read the problem carefully. Make sure you understand what is given and what is unknown. 2. If possible, make a sketch or diagram. Label the various parts. 3. Decide on the variable that must be maximized or minimized. Express that variable as a function of one other variable. 4. Find the domain of the function. 5. Find the appropriate derivative. 6. Find the critical numbers for the function. 7. If the domain is a closed interval, evaluate the function at the endpoints and at each critical number to see which yield the absolute maximum or minimum. If the domain is an open interval, apply the critical point theorem when there is only one critical number. If there is more than one critical number, evaluate the function at the critical numbers and also find the limit as the endpoints of the interval are approached to determine if an absolute maximum or minimum exists at one of the critical points.

2 Find two nonnegative numbers x and y for which 2 x  y 30 , such that xy is maximized.

An open box is to be made by cutting a square from each corner of a 3-ft by 8-ft piece of cardboard and then folding up the sides. What size square should be cut from each corner in order to produce a box of maximum volume?

2 A rectangular enclosure of 9, 408 m is to be built. One side of the enclosure will be flush against a long building and will not require any fencing. The side opposite the building will be constructed in a manner that will cost $6 per meter, while the other two sides will cost $4 per meter. Find the dimensions that will minimize cost.

A local club is arranging a charter flight to Hawaii. The cost of the trip is $542 each for 80 passengers, with a refund of $5 per passenger for each passenger in excess of 80. Find the number of passengers that will maximize the revenue received from the flight. Then find the maximum revenue.

Epidemiologists have found a new communicable disease running rampant in College Station, Texas. They estimate that t days after the disease is first observed in the community, the percent of the population infected by the disease is approximated by

p t 

20t 3  t 4 1000

for 0 t 20 . After how many days is the percent of the population infected a maximum? What is the maximum percent of the population infected?...