Math 1271, Summer 2010, Worksheet 15.11. Two highways meet at right angles in a certain town. Both highways are exactly straightlines. Two cars leave the intersection of the highways at exactly the same time. One car istraveling east at 50 mph and the other car is traveling north at 70 mph. At what rate is thedistance between the two cars increasing 3 hours after they leave the intersection?2. A very long 90 ft. ladder rests against a vertical wall. If the bottom of the ladder slidesaway from the wall at a rate of 6 ft. per second, how fast is the top of the ladder slidingdown the wall when the bottom of the ladder is 54 feet from the vertical wall?1Math 1271, Summer 2010, Worksheet 15.21. Show that f (x) =xx2+9is increasing at x = 1 and decreasing at x = 4.2. Show that f (x) =x2−9x2+9is increasing for each value of x such that 1 < x < 10.3. For what values of x are each of the following functions increasing? For what values ofx are each of the following functions decreasing?(a) f(x) = x3− 9x2− 48x + 24 (b) g (x) =√25 − x24. Sketch a graph of a function which satisfies all of the following conditions:(a) f0(x) > 0 for −2 < x < 4 (b) f0(x) < 0 for −2 > x and x >
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