2.762 x8- (1 point) Consider the function f(x) = (a) f is increasing forx E (b) f is decreasing for x e (c) The local maxima off occur at x = (d) The local minima off occur at x = 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. (1 point) Consider the function f(x) = 6x2 +5 (a) f is concave up for x E (b) f is concave down for x E (c) The inflection points of f occur at x = Note: Input U, infinity, and -infinity for union, co, and -co, respectively. If there are multiple answers, separate them by commas. If there is no answer, input none.(1 point) Consider the function f(x) = 2x + g. (a) Find all critical numbers c off. c (b)f is concave up forx E (c) f is concave down for x E (d) Using the 2nd derivative test, the local maxima off occur at x = (e) Using the 2nd derivative test, the local minima off occur at x = 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. (1 point) Suppose g(x) = (foo)2 where f is positive and concave up for all x E I. (81))\" \"(x) > on I. (b) g\" (x) = 2(A2 + B f\"(x)), whereA = and B = (G) g\"(x) > on I . (d) g(x) is on I. Note: Input CU, CD, x), f'(x), and f"(x) for concave up, concave down, f(x), f ' (x), and f \"(x), respectively. (1 point) Consider the function f(x) = 7+ ex (a) f'(x) = (b) f is increasing for x E (c) f is decreasing for x E (d) The local minima of f occur at x = (e) The local maxima of f occur at x = (1) f "(x ) = (9) f is concave up for x E (h) f is concave down for x E (i) The inflection points of f occur at x = Note: Input U, infinity, and -infinity for union, co, and -co, respectively. If there are multiple answers, separate them by