Question 1 Not yet answered Marked out of 5.00 Flag question Let f be the function defined on R by f(x) = 8x3 + 81x2 - 42x - 8. x = -7 is a critical number of f. Select one: O True O FalseQuestion 2 Not yet answered Marked out of 5.00 P Flag question If f'(x) = (x - 1 )e*, then the function f is increasing on the interval (1, +co). Select one: O True OFalse Question 3 Not yet answered Marked out of 5.00 P Flag question Let f(x) = 6x- - x'. The point x = 0 is a critical number of f. Select one: O True OFalseQuestion 4 Not yet answered Marked out of 5.00 t7 Flag question The Absolute minimum of the function f(x) = x2 x + g on [2, 2] is f(0) = g Select one: 0 True 0 False Question 5 Not yet answered Marked out of 5.00 Flag question Let f be the function defined on the closed interval [-3, 0] by : f(x) = 1-ex+2x Select one: The absolute maximum of f is reached at x = -1. O x = 0 is a critical point of f. None of these O x = -2 is a critical point of f. The absolute minimum of f is reached at x =-3The graph of a function f is given below. What are the intervals on which f is decreasing? Select one: None of these Q6 O (1/2, 3) O (-00, +00) O (3, +00) O (-00, 1/2)Question 7 Not yet answered Marked out of 5.00 'F' Flag question Which of the following statement is true for the function f (x) = (1c2 3)e' . Select one: O f (0) = 3 is a local maximum. 0 f is increasing on [-2.0]. O x = -3 is a critical number off. 0 None of the others 0 ) = 0 is a local maximum. Question 3 Not yet answered Marked out of 5.00 if? Flag question In which of the following intervals the function 150') = x2 - 8x + 3 is decreasing? Select one: 0 (4.00) O (-5.00) 0 (0,00) 0 None of the other choices. 0 (001 4) Question 9 Not yet answered Marked out of 60.00 17 Flu; question Work Problem [60 points]: Solve the following questions. Write step by step solutions and instify your answers. 1) [20 Points} Find the critical numbers of the function f(x) = x3 '75:? + 12x. 2) [20 Rims] Find where the function Jx) = x $33 is increasing or decreasing. Find also the local extreme values of f. 3) [20 Points] Discuss the curve f(x) = is4 33:3 with respectto concavity, points of inection. and local maximum and