8 Questions in Exam 2 - Calculus | MATH 1120, Exams of Calculus

Download 8 Questions in Exam 2 - Calculus | MATH 1120 and more Exams Calculus in PDF only on Docsity! Math 1120, Section 7 Calculus Test 2 October 19, 2006 Name The total number of points available is 148. Throughout this test, show your work. 1. (9 points) Let f(x) = x3 − 2x− 3. (a) Compute f ′(x) (b) What is f ′(2)? (c) Use the information in (b) to find an equation for the line tangent to the graph of f at the point (2, f(2)). 2. (12 points) Consider the function f defined by: f(x) =  x + x3 if x < 1 2 if x = 1 2x1/2 if x > 1 (a) Is f continuous at x = 1? (b) What is the slope of the line tangent to the graph of f at the point (4, 4)? (c) Find f ′(−3) 1 Math 1120, Section 7 Calculus Test 2 3. (15 points) If a ball is thrown vertically upward from the roof of 212 foot building with a velocity of 48 ft/sec, its height after t seconds is s(t) = 212 + 48t− 16t2. (a) What is the height the ball at time t = 0? (b) What is the velocity of the ball at the time it reaches its maximum height? (c) At what time is the velocity zero? (d) What is the maximum height the ball reaches? (e) What is the velocity of the ball when it hits the ground (height 0)? 4. (10 points) The cost of producing x units of stuffed alligator toys is C(x) = −0.003x2 + 6x + 6000 for 0 ≤ x ≤ 1000. (a) Find the marginal cost at the production level of 1000 units. (b) Find the (incremental) cost of producing the 1000th toy. 2