Mathematics Department | CoAS | Drexel University
13.1 and 13.2 Problems13.1Find the intervals where the function is (a) increasing, or (b) decreasingFor each function find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing13.y=2.3+3.4x-1.2x215.fx=23x3-x2-24x-417.fx=4x3-15x2-72x+523.y=6x-945. A country realty group estimates that the number of housing starts per year over the next three years will beHr=3001+0.03r2Where r is the mortgage rate (in percent). Where is H(r) increasing?Where is H(r) decreasing?50. The number of people P(t) (in hundreds) infected t days after an epidemic begins is approximated byPt=10 ln?(0.19t+1)0.19t+1When will the number of people infected start to decline?13.2 problems Find the locations and values of all relative extrema for the functions with graphs as followsFind the x value of all points where the functions defined as follows have any relative extrema. Find the values of any relative extrema15.fx=x3+6x2+9x-819.fx=x4-18x2-421.fx=3-8+3x2/325.fx=x-1x29.fx=x2ex-346. The total profit P(x) (in thousands of dollars) from the sale of x units of a certain prescription drug isPx=ln-x3+3x2+72x+1, [0,10] Find the number of units that should be sold in order to maximize the total profit.What is the maximum profit?56.After a great deal of experimentation, two Atlantic Institute of Technology senior physics majors determined that when a bottle of French champagne is shaken several times, held upright, and uncorked, its cork travels according tost=-16t2+64t+3,Where s is the height (in feet) above the ground t seconds after being released. How high will it go?How long is it in the air? ................
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