Find all critical numbers c of f(a:) : 3:r:2 -+ 18:1: 1468. Note: If there is more than one critical number, separate them by a comma. Consider the graph of f(:1:) given below. (a) Analyzing the graph, if g(m) = f(:1:), then 9(33) is increasing for a: E (b) Analyzing the graph, if h'(a:) : f(:L'), then Mm) is increasing for m E Note: Input U, infinity, and -infinity for union, 00, and 700, respectively. Clicking on the graph will enlarge it. Each tick on the graph is 1 unit. Consider the graph of f (9:) given below. I; = Nu) (a) Analyzing the graph, if g(a:) = f(:12), then 9 is decreasing for m E (b) Analyzing the graph, if h'(a:) : f(:13), then It is decreasing for :r: E Note: Input U, infinity, and -infinity for union, co, and 700, respectively. Consider the function f(:c) = 2m3 + 6:122 I 144:1: 3. (a) f is increasing for a: E (b) f is decreasing for :1: E (c) The local maxima of f occur at m : (d) The local minima off occur at a: : Note: Input U, infinity, and -infinity for union, co, and 00, respectively. If there are multiple answers, separate them by commas. If there is no answer, input none. 2:132 506- Consider the function f(:r,) : (a) f is increasing for at: E (b) f is decreasing for a: E (c) The local maxima of f occur at :1: = (d) The local minima of f occur at :1: = Note: Input U, infinity, and -infinity for union, co, and oo, respectively. If there are multiple answers, separate them by commas. If there is no answer, input none