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Optimization problems

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Useful for: IB Math AA SL & HL IB Math AI SL & HL AP® Calculus (intro)

Learn it Write the quantity to maximize or minimize as a function of one variable (use the constraint to remove the other), differentiate, set f′ = 0, and check it's a max or min and makes sense in context.

Example: An open box from a 30 cm square sheet by cutting squares of side x from each corner. Max volume?

  1. V = x(30 − 2x)², 0 < x < 15.
  2. V′ = (30 − 2x)(30 − 6x) = 0 → x = 5.
  3. V = 5(20)² = 2000 cm³.

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