Calculus -- Notes
3.7 Optimization Problems
Solving Max / Min Problems
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Assign symbols to all given quantities and ones to be determined. Make a sketch.
Write a Primary Equation for the quantity to be maximized or minimized.
Reduce the Primary Equation to one having a single independent variable (secondary equation).
Determine the domain of the primary equation.
Determine the desired max or min value.
Use the Second Derivative Test to verify max or min status.
EX 1: The product of two positive numbers is 192 and the sum of the first plus three times the second
is a minimum. Find the two numbers.
EX 2: A rancher has 200 ft of fencing with which to enclose two adjacent rectangular corrals. What
dimensions should be used so that the enclosed area will be a maximum?
EX 3: Find the points on the graph of y = x that are closest to the point (0, 2).
EX 4: A manufacturer wants to design a box having a square base and surface area 432 in2. What
dimensions will produce a box with maximum volume?