Complete the following exercises. Show appropriate work/reasoning and include appropriate units for full credit You may only use techniques that have been developed to this point in the course. 1. Determine the critical numbers for each of the following functions: a. f(x) = 2x3 _ 5x2 7x+ 6 b. s(t)=3\/t276t+8+4 c. Mp) = 8 cos(3p) + 12;), for 0 S p S 27: 2. Determine the absolute maximum and minimum values for each function over the given interval. Note that these are the same functions used in exercise 1. You may use your results from exercise 1. a. f(x) = 2x3 5x2 7x + 6 on [0.4] b. 5(t) = 3ch 6t + 8 + 4on [0.7] 3. Given the function f(x) = 2x3 13x2 10x + 30 a. Consider for) on [1.7]. Are the conditions for Rolle's Theorem met? If they are, find the appropriate "c" valuels) that satisfy the conclusion ofthe theorem. b. Consider f(x) on [0,7]. Are the conditions for the Mean Value Theorem met? If they are, find the appropriate "c" valueis} that satisfy the conclusion of the theorem. 4. Given the function f(x) = ctr"C(x2 3) 3. Determine the intervals where f(x) is increasing, and the intervals where f(x) is decreasing. b. Identify any relative extrema (as ordered pairs) 5. Given the function f(x) = 3x5 30:364 + 401:3 a. Determine the intervals where f(x) is concave up, and the intervals where f(x) is concave down. b. Identify any inflection points (as ordered pairs)