(1 point) Consider the graph of f(r) given below. (a) Analyzing the graph, if g(x) = f(x), then g(x) is increasing for I E (b) Analyzing the graph, if h'(x) = f(x), then h(x) is increasing for I E Note: Input U, infinity, and -infinity for union, oo, and -oo, respectively. Clicking on the graph will enlarge it. Each tick on the graph is 1 unit.(1 point) Consider the graph of f ( ) given below. (a) Analyzing the graph, if g(x) = f(x), then g is decreasing for I E (b) Analyzing the graph, if h'(x) = f(x), then h is decreasing for I E Note: Input U, infinity, and -infinity for union, oo, and -oo, respectively.(1 point) Consider the function f(x) = -4x3 + 1812 - 24x + 2. (a) f is increasing for I E (b) f is decreasing for I E (c) The local maxima of f occur at = = (d) The local minima of f occur at x = Note: Input U, infinity, and -infinity for union, oo, and -oo, respectively. If there are multiple answers, separate them by commas. If there is no answer, input none.(1 point) Consider the function f(I) - 2 (a) f is increasing for I E (b) f is decreasing for a E (c) The local maxima of f occur at x = (d) The local minima of f occur at x = Note: Input U, infinity, and -infinity for union, oo, and -oo, respectively. If there are multiple answers, separate them by commas. If there is no answer, input none.(1 point) Consider the function f(x) = 6x2 - 214 (a) f is increasing for I E (b) f is decreasing for I E (c) The relative maxima of f occur at r = (d) The relative minima of f occur at a = Note: Input U, infinity, and -infinity for union, oo, and -oo, respectively. If there are multiple answers, separate them by commas. If there is no answer, input none.(1 point) Consider the function f(x) = -2x3 + 3912 - 2401 + 6. (a) Find all critical numbers c off. c = (b) f is increasing for I E (c) f is decreasing for I E Note: Input U, infinity, and -infinity for union, oo, and -oo, respectively. If there are multiple answers, separate them by commas. If there is no answer, input none.(1 point) Consider the function f(x) = 2x3 - 33x2 + 1681 + 9. (a) f has a local minimum at the point ( |7,254 (b) f has a local maximum at the point ( 4,281(1 point) Consider the function f(x) = -5x2 + 6x - 11. (a) Find all critical numbers c of f. c = 3/5,-46/5 (b) The local maxima values of f are: 3/5 (c) The local minima values of f are: -46/5 Note: If there are multiple answers, separate them by commas. If there is no answer, input none.(1 point) Find all critical numbers c of f(x) = -10x2 + 11x - 96. C = Note: If there is more than one critical number, separate them by a comma.(1 point) Find all critical numbers c of f(x) = 6x3 - 27x2 - 180x + 1. C = Note: If there is more than one critical number, separate them with a comma.(1 point) Find all critical numbers c of f(x) = (6x + 5)e-3x Note: If there is more than one critical number, separate them by a comma