Exercise 6.5.1 Consider the function f : I - R given by f (20) = 23 - 3x. Find if global extrema exist and where they occur for each of the following cases: (i) I = (-00, 0), (ii) I = (-3,4], (iii) I = [-2, 1]. Exercise 6.5.2 Find if global extrema exist and where they occur for each of the following functions. Hint: For the first case below, it is not necessary to find the stationary points of the function. f : R - R defined by f(x) =25 - 3x4+ 7x - 18, g : R -+ R defined by g(x) = 24 + 6x2 + 5, h : [-2, 3] - R defined by h(x) = ex -x. Exercise 6.5.3 Following the methodology presented in subsection 6.1 of the Lecture Notes, sketch the graph of the function f : (-0o, 0) U (0, 00) - R defined by f(x) = x +; Exercise 6.5.4 Consider the profit function 7 : [0, 2] - R defined by TT (2) = R(x) - C(x) where R(x) = 4x is the revenue function and C(x) = 23 - x2 - 5x is the cost function. Find the maximum value of 7(x) on [0, 2] and the corresponding quantity x