Problem 4 [12 points]: Consider the following function, defined on (-2, 2]: x2 – X, -2 < x < -1, f(x) = = x2 х +1, -1 <

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Problem 4 [12 points]: Consider the following function, defined on (-2, 2]: x2 – X, -2 < x < -1, f(x) = = x2 х +1, -1 < x < 2. 2 (a) Find the global (absolute) minimum value of f(x) on (-2, 2], and the point where it occurs. If f(x) has no global minimum, explain why. - (b) Next, we consider the above function f = f(x) on a smaller interval (-2,0). (i) Are the hypotheses of the Mean Value Theorem satisfied by the function f on the interval (-2,0]? (ii) Does the conclusion of the Mean Value Theorem hold for the function f on the interval (-2,0]?