TEST - Applications of Derivatives
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7/30/2019 TEST - Applications of Derivatives
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UNIT 4: APPLICATIONS OF DERIVATIVES TEST
NAME: _____________________________________________ DATE: ____________________ 1.
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UNIT 4: APPLICATIONS OF DERIVATIVES TEST
NAME: _____________________________________________ DATE: _______________
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UNIT 4: APPLICATIONS OF DERIVATIVES TEST
NAME: _____________________________________________ DATE: _______________
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UNIT 4: APPLICATIONS OF DERIVATIVES TEST
NAME: _____________________________________________ DATE: _______________
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UNIT 4: APPLICATIONS OF DERIVATIVES TEST
NAME: _____________________________________________ DATE: _______________8.
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UNIT 4: APPLICATIONS OF DERIVATIVES TEST
NAME: _____________________________________________ DATE: _______________10.
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UNIT 4: APPLICATIONS OF DERIVATIVES TEST
NAME: _____________________________________________ DATE: _______________
11. If 1200 cm2 of material is available to make a box with a square base and an open top, find the largest possible
volume of the box.
12. Gravel is being dumped from a conveyor belt at a rate of 30 ft3/min, and its coarseness is such that it forms a pile in
the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when
the pile is 10 feet high?
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UNIT 4: APPLICATIONS OF DERIVATIVES TEST
NAME: _____________________________________________ DATE: _______________
13. Determine whether or not the Mean Value Theorem can be applied to f(x) = 2 + 1/x on the interval
[3, 4]. If so find the value(s) ofc guaranteed by the theorem.
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UNIT 4: APPLICATIONS OF DERIVATIVES TEST
NAME: _____________________________________________ DATE: _______________
14. Let fbe the function defined by f(x) = x3 + 3x2
a) Find the interval(s) on which fis increasing. Justify your answer.
b) Find the x and y coordinates of all relative maximum points. Justify your answer.
c) Find x and y coordinates of all relative minimum points. Justify your answer.
d) Find the interval(s) on which fis concave downward. Justify your answer.e) Using the information found in parts a d, (not your calculator) neatly sketch the graph off.
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