MAC2233_2010_Summer_T2A

MAC2233_2010_Summer_T2A - Name_ Date_ MAC 2233: Exam 2...

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Name_______________________________________________________________________ Date__________________ MAC 2233: Exam 2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question Provide an appropriate response. 1) Find dy/dx by implicit differentiation. x 3 + y 3 = 5 A) dy dx = - y 2 x 2 B) dy dx = y 2 x 2 C) dy dx = - x 2 y 2 D) dy dx = x 2 y 2 Evaluate dy/dt for the function at the point. 2) xy 2 = 4; dx/dt = - 5, x = 4, y = 1 A) - 5 8 B) - 8 5 C) 8 5 D) 5 8 Solve the problem. Round your answer, if appropriate. 3) A spherical balloon is inflated with helium at a rate of 110π ft 3 /min. How fast is the balloon's radius increasing when the radius is 5 ft? A) 1.10 ft/min B) 2.75 ft/min C) 0.22 ft/min D) 3.30 ft/min Identify the critical points and find the maximum and minimum value on the given interval I. 4) f(x) = x 2 + 18x + 81; I = [ - 18, 0] A) Critical points: - 18, 0, 9; maximum value 81; minimum value 0 B) Critical points: - 9; maximum value 18; minimum value 0 C) Critical points: - 18, 0, 81; minimum value 0 D) Critical points: - 18, - 9, 0; maximum value 81; minimum value 0 Use the Concavity Theorem to determine where the given function is concave up and where it is concave down. Also find all inflection points. 5) q(x) = 3x 3 + 2x + 8 A) Concave down for all x; no inflection points B) Concave up on ( -∞ , 0), concave down on (0, ); inflection point (0, 8) C) Concave up for all x; no inflection points D) Concave up on (0, ), concave down on ( -∞ , 0); inflection point (0, 8) Solve the problem. 6) Given the distance function, s(t)
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MAC2233_2010_Summer_T2A - Name_ Date_ MAC 2233: Exam 2...

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