Question: 2. Suppose that f(x) = x3 + ax + bx + c, for some unknown constants a, b, and c, has a local minimum of

2. Suppose that f(x) = x3 + ax + bx + c, for some unknown constants a, b, and c, has a local minimum of 4 at x = 3, and an inflection point at x = 2. Determine f(1). (Hint: See Practice Problem 10 in 4.3.) 3. A box with a square base and open top must have a volume of 32,000 cm2. Find the dimensions of the box that minimize the amount of material used. (Hint: Minimizing the amount of material translates to minimizing the Surface Area of the box (with no top!))

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