MA 121 - 003 Review for Test #2 Fall 2019 Instructions: This is a review guide. Questions on the actual test may or may not resemble the questions below. Do not forget to review all examples from class and your Webassign problems. You may not use a graphing calculator or a calculator that does calculus. A four function or scientific calculator is permitted. 1. Find f 0 (x) for (a) f (x) = p 3 5x (b) f (x) = (5 (d) f (x) = (5x2 + 3x 2)3 (6x + 1)2 p (e) f (x) = x x2 + 1 ✓ ◆3 2 2x + 3 (f) f (x) = 5x 1 3 x)2 (2x 1)5 2 (c) f (x) = x8 +x8 2. An object’s position above the ground, s(t), in meters, after t seconds is given by s(t) = t3 9t2 + 24t. (a) What is the position of the object at time t = 3 seconds? (b) Find the velocity of the object as a function of t. (c) Find the object’s acceleration at any time t. (d) When is the object at rest (i.e. when is it not moving)? (e) Find the acceleration of the object for each time the object is at rest. 2 3. Write an equation of the tangent line to the graph of f (x) = xx +13 at x = 2. 4. Find y 00 if y = x3 2 x. 5. Find all holes, asymptotes, and intercepts (if there are any) of h(x) = x3 x x2 2 2x . 3 6. (a) Find all asymptotes and intercepts of y = 2x x + 5 . Then, use the first derivative test to determine where f (x) is increasing and decreasing. Use this information to graph f (x). 3 (b) Given the function g(x) = 8 2x + 13 , use the first and second derivative tests to find intervals 3x where g(x) is increasing, decreasing, concave up, and concave down. Find all relative extrema and points of inflection. Graph g(x). 7. Find all absolute extrema of f (x) = 23 x3 + 4x2 + 6x 5 on the interval [ 2, 0]. 8. A lifeguard needs to rope o↵ a rectangular swimming area in front of Long Lake Beach, using 180 yds of rope and floats. Note that the shoreline is one side of the rectangle, so the lifeguard will not need rope for that side. What dimensions of the rectangle will maximize the area? What is the maximum area? 1