# cubic centimeters per minute

Math 28, Summer 2021 Name: Quiz 3 Instructions: There are 3 problems. Read each problem carefully. Label answers appropriately. Show all your work. Submit your work on Canvas as a single PDF under Assignments, Quiz 3 Submission. [9] 1) Find the derivative of each of the following functions. You do not need to simplify your answers. a) g(x) = 2x x2 + 1 b) h(x) = x3 log(x4 + 1) c) F (x) = p ln(x2 + 1) 1 [7] 2) Suppose xy 2 − y − 2 = 0. Using implicit differentiation, find tangent line(s) to the graph when x = 1. dy and the equation(s) of the dx [4] 3) Water is pumped into a spherical balloon at a rate of 1000 cubic centimeters per minute. How fast is the radius of the balloon changing when the radius is 5 centimeters? Include units in your answer. 2

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