Exam 4: Applications of the Derivative

After the economy softened, the sky-high office space rents of the late 1990s started to come down to earth. The function R gives the approximate price per square foot in dollars, R(t), of prime space in Boston's Back Bay and Financial District from 1997 ( ) through 2000, where . What was the highest office space rent during the period in question? Hint: Use the quadratic formula.

Find the inflection points, if any, of the function. Otherwise, answer no solution.

An efficiency study conducted for a company showed that the number of devices assembled by the average worker t hr after starting work at 8 A. M. A.M. is given by At what time during the morning shift is the average worker performing at peak efficiency? At __________

The total worldwide box-office receipts for a long-running movie are approximated by the function where is measured in millions of dollars and x is the number of years since the movie's release. Select the graph of the function T.

Find the absolute maximum value and the absolute minimum value, if any, of the given function. on [1, 4]

Find the relative maxima and relative minima, if any, of the function.

Determine where the function is concave upward.

Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.

The Mexican subsidiary of ThermoMaster manufactures an indoor-outdoor thermometer. Management estimates that the profit (in dollars) realizable by the company for the manufacture and sale of x units of thermometers each week is . Find the intervals where the profit function P is increasing and the intervals where P is decreasing.

Find the dimensions of a rectangle of area 144 sq ft that has the smallest possible perimeter.

Find the absolute maximum value and the absolute minimum value, if any, of the given function.

Find the horizontal and vertical asymptotes of the graph of the function.

Find the absolute maximum value and the absolute minimum value, if any, of the given function.

Find the horizontal and vertical asymptotes of the graph of the function.

Find the relative maxima and relative minima, if any, of the function. Otherwise, answer none. Relative minima: __________ Relative maxima: __________

If an open box has a square base and a volume of 864 and is constructed from a tin sheet, find the dimensions of the box, assuming a minimum amount of material is used in its construction.

A city's main well was recently found to be contaminated with trichloroethylene (a cancer-causing chemical) as a result of an abandoned chemical dump leaching chemicals into the water. A proposal submitted to the city council indicated that the cost, measured in millions of dollars, of removing x% of the toxic pollutants is given by . Find the vertical asymptote of C(x). Is it possible to remove 99% of the toxic pollutant from the water?

Determine where the function is concave upward and where it is concave downward.

Find the absolute maximum value and the absolute minimum value, if any, of the given function.

Show that the function has no relative extrema on .