6:13 Back HW 9 - written component 3 of 3 Question 1 Determine whether Rolle's Theorem applies to the following functions on the given interval. If so, find the point(s) guaranteed to exist by Rolle's Theorem. If the theorem does not apply, clearly explain why. (a) f(x)=x³-x²-5x-3, on [-1,3] (b) f(x)=x+(1-x)2/3, on (-1,3] (c) f(x) = 1 − |x|, on [−1, 1] Question 2 Let f(x)=3x+cosx-sin. Show that f(x) has an unique root. Question 3 Assume f is a differentiable function on [1, 5]. Assume that f(1) = -2 and that f'(x) ≥ 12 for all r = [1,5]. What is the smallest f(5) can be? Question 4 Determine whether M.V.T. applies to the following functions on the given interval. If so, find the point(s) guaranteed to exist by M.V.T.. If the theorem does not apply, clearly explain why. (a) f(x)=2x+√x-1, on [1,5] 2-3 (b) f(x) = on [0,4] 1- (c) f(x)=√3x+2cos z, on [0,2] (d) f(x) = x²-³, on [−1,1] 20