Problem 6. Show that the function f(x) = 13 - 3x + 2 satisfies the mean the theorem. value theorem on the interval [-2, 2], then find all values of c which satisfy Problem 7. Show that the function f(r) = sin () satisfies the Rolle's theorem. theorem on the interval [7, "], then find all values of c which satisfy the Problem 8. Consider the function f(x) = 21 - 212 + 3 (a) Use a sign chart to find the intervals of increase / decrease for f(x). (b) Find the relative maximums and minimums for f (x). (c) Use a sign chart to find the intervals of concave up/ down for f(x). (d) Find any points of inflection that exist. Problem 9. For the function f(x) = xle- do parts (a) through (d) from problem 8 Problem 10. Find each of the following limits. 1. lim 2 + 12 co 1 - 2x2 1 - sin 0 2. lim r- 1 + cos 20 In r graph of f'(2) is Blow 3. lim in for . I-70+ local 4. lim I-H 5. lim (1 + 3x)2/1 6. lim x tan (1/2) 2