7. Find if any local maximum and local minimum values of the function g(x) = 2x + 4x-1 by using the methods we discussed in this class. Give the exact answers. DO NOT give decimal approximations. (a) Local maximum value if any. (b) Local minimum value if any. 8. Consider the function f(x) = x5(x + 7)? in the interval [-14, 12]. Find the critical numbers of the function, intervals where the function is increasing and decreasing by using the methods we discussed in this class. a. Find the critical numbers of the above function. b. Find the interval(s) where the function is increasing. c. Find the interval(s) where the function is decreasing. d. Find the interval(s) on which the function is positive. e. Where does the function achieve its minimum? 9. Graph of the function f(x) is given below. (a) At the point shown on the function below, which of the following is true. a. f' > 0, f" 0, f" > 0 d. f' 0 Give the approximated value. (b) f' ( - 3) = 10. Determine the signs (positive, negative, or zero) of the function y = f(x) (shown in the graph) and f'(x) and f"(x) when x = 2. a. What is the sign of f (2)? b. What is the sign of f'(2)? C . What is the sign of f"(2)