Prof. Yeung Date: Chapter 3.4- 3.8 Zoom Proctor Test MA 120 Spring 2022 Absolute Maxima and Minima: 1. Use the methods discussed in Ch 3.4 to find the absolute and minimum values of f, if any, on the given interval, and state where those values occur. Show all your work in order to receive full credit. a) Given f(x) = =x3 + 2x2 - 80x + 9, on the interval [-8,8] b) Given f(x) = x - sin x, on the interval [- 7.7] Applied Maximum Problem: 2. Find the point on the function f (x) = =x2, which is closest to the point (3, -3). Hint: The distance formula is d = (x2 -x1)2 + (12->1)? Rectilinear Motion: 3. The function s(t) = 6t3 - 8t2 + 6t + 10 describes the position of a particle moving along a coordinate line, where s is in feet and t is in second. Assume t 2 0. a) Find the velocity and acceleration function. b) When is the particle speeding up? Slowing down? c) At what time(s) is the particle stopped? d) Find the position of the particle and the velocity when the acceleration is at 0. 4. The graph in figure A shows the velocity versus time graph of a particle and figure B shows the acceleration versus time graph of the same particle in figure A. Use the information from both fig to identify the motion of the particle when it is traveling in a positive direction, negative direction momentarily stopped. Determine when it is speeding up and slowing down (if any)? 20 20 15 15