All work must be shown. Credit will not be given for inst answers 1. Complete the following statements, if SO) is a position or displacement function. a. Average velocity on an interval [a, b] is equal to b. Instantaneous Velocity is equal to c. Instantaneous Acceleration is equal to C]. Speed is equal to e. To detennine when the velocity is decreasing, f. An object is speeding up on an interval when 2. A particle moves along a straight line with equation of motion, 4:3 50') = ? 101'2 + 241' 0 S 1' $10, where S(t) is measured in feet and I in seconds. When is the velocity zero? When is the position increasing? When is the acceleration zero? When is the velocity decreasing? What is the position of the particle when the velocity is zero? When does the particle change direction? an? FL? 9'? . The population of the state of Georgia (in thousands) from 1995 (t = 0) is modeled by the function p(t) = 4.27:2 +10: + 7055 . a. Determine the Population of Georgia in 2000 b. Determine the average growth rate from 1995 to 2005. o. What was the Instantaneous growth rate for Georgia in 1997 and 2005? d. When will the population decrease? . Find the derivative of the following by applying the chain Rule and simplify. a. f(x) = [m] b. f(x) = {)(9x + '1')2 c. g(x) = set:2 (a't ) 3 . Find the equation of the tangent line to the graph of f(x) = [L] at x+3 f(x)= [ac+3) . The following limit represent the denition of the derivative of a function at a point a sec %+ h] J5 lim 1410 h a. Find a possible function f (x) and a. b. Then use a differentiation rule to evaluate the limit. . Find the second derivative of the following function and simplify. a. 1r11(t)=(:c2 1)'1 b. h(x) = sin(x2)