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Math 2250 HW #10 Due 1:25 PM Friday, October 21 Reading: Hass §4.1–4.3 Problems: Do the assignment “HW10” on WebWork. In addition, write up solutions to the following two problems and hand in your solutions in class on Friday. 2 1. Find the absolute maximum and minimum values of the function g(x) = e−x subject to the constraint −2 ≤ x ≤ 1. 2. Find all local maxima and minima of the curve y = x2 ln x. 3. A general cubic function has the form f (x) = ax3 + bx2 + cx + d where a, b, c, and d are constants. (a) Give examples that demonstrate such functions can have 0, 1, or 2 critical points. (b) Show that no cubic function can have more than 2 critical points. (c) How many local extreme values (maxima and/or minima) can a cubic function have? 1