Question 1. Consider the following function. Rx) = -5x3+ 15x + 4 (a) Find the critical numbers of f. (Enter your answers as a comma separated list.) x - -1.1 (b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter ONE.) increasing (-1,1) decreasing (-00. - 1).(1,00) (c) Apply the First Derivative Test to Identify the relative extremum. (If an answer does not exist, enter DNE.] relative maximum (x, ) = ( relative minimum (X, V) = (1 Question 2. Identify the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.) h(x) = 75x - x3 Increasing decreasing Question 3. Consider the following function. (x] - x* - 32x + 9 (a) Find the critical numbers of /. (Enter your answers as a comma-separated list.) * = (b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter ONE.) Increasing decreasing (c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DINE.) relative maximum (x, p) -( relative minimum (x x) - ()Question 4. Determine whether Rolle's Theorem can be applied to / on the closed interval (a, b]. (Select all that apply.)) ((x] = -x + 9x. [0, 9] O Yes, Rolle's Theorem can be applied. D No, bix is on the closed Interval [a, ] D No, because / is not differentiable in the open interval (a, b). O No, because /ta] . "Tal. if Holle's Theorem can be applied, find all values of c in the open interval (a, b) such that ITc) = 0. (Enter your answers as a comma separated list. If Rolle's Theorem cannot be applied, enter NA] Question 5. Determine whether the Mean Value theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) (x) = 3x . [1. 2] O Yes, the Mean Value Theorem can be applied. O No, because I is not con he closed Interval [s, D] O No, because I is not differentiable in the open interval (o. b]. 0 None of the above. If the Mean Value Theorem can be applied, find all values of c in the open interval (a, b] such that ? [c) = ) - 21. (Enter your answers as a comma separated list. If the Mean Value Theorem cannot be applied, enter NA.) Question 6. Consider the following function and closed interval. (x) - 4x] [1, 2] Is / continuous on the closed interval [1. 217 O TH No If / is differentiable on the open interval (1, 2), find / (x). [If it is not differentiable on the open interval, enter ONE.) Find (1) and (2). Find !18) - Kal four [a, b) = (1, 2]. b - a b- a Determine whether the Mean Value Theorem can be applied to / on the closed interval [a, b]. (select all that apply.) O Yes, the Mean Value Theo um can be applied. No, because / is not com Unyous on the closed Interval [a. b]. No, because / is not differentiable in the open interval fa, bj. None of the above. If the Mean Value Theorem can be applied, find all values of c in the open interval (s. D] such that / c] - MD) In23. If the Mean Value Theorem cannot be applied, explain why not. (Enter your answers Is a comma-separated list. If the Mean Value Theorem cannot be applied, enter NA.}Question 7. Determine whether the Mean Value Theorem can be applied to f on the closed interval [a, b]. If the Mean Value Theorem can Be applied, find all values of c in the open interval [a, b) such that "ye) = 101-10.If the Mean Value Theorem cannot be applied, explain why not. (x) = 3/, [0. 1] Can the Mean Value Theorem be applied? (Select all that apply ] O No, / is not continuous on [a, b]. O No. /is not differentiable on (a, bj. O None of the above. If the Mean Value Theorem can be applied, find all values of c in the open interval (a, b] such that / Te) - PEPPER. [Enter your answers as a comma separated list. IF the Mean Value Theorem cannot by applied, enter NA ] Question 8. Determine whether Rolle's Theorem can be applied to / on the closed interval (o, b]. (Select all that apply.) (x) - x - 10r + 24. [4, 6] O Yes, Rolle's Theorem can be applied. O No, because / Is not continuous on the closed interval [a, &] No, because I is not differentiable in the open interval (a, b]. O No, because its) # /to). If Rolle's Theorem can be applied, find all wakes of c in the open interval (s, b) such that /Tc) - 0. (Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter NA.)