Fall 2014 – MATH 151, Sections 549-551
Quiz #5
PART I: Multiple Choice. Read each problem carefully and work it out in the space
provided. Put a box around the answer you believe best answers the question. Calculators are not allowed.
p
√
3
Problem 1 (4 pts). Let s(t) = 1 + t. Find s0 (4).
(a)
1
√
3 3 16
(b)
1
√
6 3 16
(c) s(t) is not differentiable at 4.
(d) None of the above.
Problem 2 (4 pts). Let f (x) =
√
x2 − 7x. Which of the following statements is false?
(a) f (x) is continuous at 0.
(b) f (x) is not differentiable at 0.
(c) f (x) is differentiable at 7.
(d) f (x) is continuous at 7.
1
Math 151 Fall 2014
Quiz #5
2
PART II: Free response. Read each problem carefully and work it out in the space
provided. Circle your final answer.
Problem 3 (6 pts). Suppose that xf (x) = cot(xf (x)). If f (2) = 6, what is f 0 (2)? [Hint:
First find f 0 (x) by implicit differentiation.]
Math 151 Fall 2014
Quiz #5
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Problem 4 (4 pts). A spherical balloon is inflating with helium at a rate of 400π cubic
feet per minute. How fast is the balloon’s radius increasing the instant the radius is 5
feet? (The volume of a sphere is given by V = 43 πr3 .)
Math 151 Fall 2014
Quiz #5
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Bonus Problem (2 pts). For which values of x is the piriform y 2 = x3 (2 − x) (see the
graph below) not differentiable?