Which of he following functions satisfy the hypotheses of the Mean Value Theorem on the given interval? f() m2m, 2a:g1 1' 2m23m3, 1 0, then f is increasing on [0, 2]. O If f' is continuous and f' (0) 0 on (a, b), the graph of f over (a, b) is choose your answer... 2.) If f" (x2 - 1) :? 2 -2 O (V3, 3(2-4/3) ) None of the other points are points of inflection (0, ; ) O (1, 0 )For which of the following functions f and points c can the second derivative test for local extrema be used to determine if f has a local maximum or minimum at x = c? f(z) = (x2 - 1)3 atc = 1. D f () = sin(x) at c = T / 2. f(z) = 12(6 - a2) - 4atc = 0. O f(z) = |22 - 1/ at c = 0.Suppose f\" is continuous on an open interval that contains a: = 0. Suppose f has local maximum at :L' = c. Then 1. necessarily f'(c) = 0 choose your answer... 2. necessarily f"(c) 0. 1. limz-+0+ In(x2+2x) In(x) type your answer... 2. lima +0+ type your answer... 8 1 sin (x)E Suppose a light is traveling through from medium 1 through medium 2 such that the angle of incidence is 6 rad and the angle of refraction is g. If the speed of light in medium 2 is % times the speed of light, what is the speed of light in medium 1? If the answer is a rational number but not an integer, type a/b, where a and b are integers with greatest common factor 1, and b > O. Ans: Speed of light in medium 1 is times the speed of light