# None of the sand is blowing away so the volume

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causing the height of the cone to decrease, while maintaining a conical shape. None ofthe sand is blowing away, so the volume remains constant. The current height of thecone is 2mand its base radius if 3m. If the height of the cone is decreasing at a rateof 0.01m/hr, then how fast is the base radius increasing?7. Consider the following function on [-3,3], along with its derivatives:[13marks]f(x) =-xx2+ 4,f(x) =x2-4(x2+ 4)2,f′′(x) =2x(12-x2)(x2+ 4)3.(a) Find the roots/zeroes and vertical asymptotes off(x) (if there are any).(b) Find the critical points off(x) and then use a sign chart to find the intervalswherefis increasing/decreasing (if there are any).(c) Find any local maximum and local minimum values (if there are any) and justifyby the first or second derivative test.Determine the absolute maximum andminimum values on [-3,3].(d) Find the intervals of concavity (if there are any).(e) Use the information in (a)-(d) to sketchf(x) on [-3,3] labeling any importantpoints. Draw your sketch neatly on the back page if you need more space.
MA103 – Midterm Test2013 FallPage 2 of 2Answers
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