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10 questions
Suppose that for a twice differentiable function f (x), f '(x) > 0 and f ''(x) > 0 on the interval (1,3). If we use a linear approximation at x = 2 to estimate f (1.9), will that estimate be an underestimate or overestimate, and why?
Underestimate since f '' > 0 on (1, 3)
Overestimate since f '' > 0 on (1,3)
Underestimate since f ' > 0 on (1, 3)
Overestimate since f ' > 0 on (1, 3)
A spherical snowball melts so that its radius decreases at a rate of 4 in/sec. At what rate is the volume of the snowball changing when the radius is 4 in?
-262π in3/sec
-247π in3/sec
-256π in3/sec
-263π in3/sec
A 5 ft ladder is leaning against a wall and sliding towards the floor. The top of the ladder is sliding down the wall at a rate of 2 ft/sec. How fast is the base of the ladder sliding away from the wall when the base of the ladder is 3 ft from the wall?
4/3 ft/sec
8/7 ft/sec
1 ft/sec
8/3 ft/sec
2
-2
1/2
-1/2
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