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Math 2250 HW #10 Due 12:30 PM Thursday, October 17 Reading: Hass §4.1–4.2 Problems: Do the assignment “HW10” on WebWork. In addition, write up solutions to the following problems and hand in your solutions in class on Thursday. 1. Find the absolute maximum and minimum values of the function f (x) = 9 − |x| subject to the constraint −1 ≤ x ≤ 3. 2. Find all local maxima and local minima of the function g(x) = x . ex2 3. Determine whether the following statements are true or false. If the statement is true, explain why. If it is false, give an example of a function which shows that it is false (called a “counterexample”). (a) If x = c is a critical point of the function f (x), then it is also a critical point of the function g(x) = f (x) + k for any constant k. (b) If x = c is a critical point of the function f (x), then it is also a critical point of the function h(x) = f (x − k) for any constant k. 1