Calculus
Lesson
18 Optimization
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Surface Area = SA = 108 in2 with a square box. What dimensions
maximize the volume of the box?
How do we know this is a max and not a min?
This is just like what we've been doing: what is x
when f(x) is a max?
what is w when V is a max?
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Another way is to see how both V and h vary with w:
Steps:
1) Get a function of one variable
2) Find extrema
3) Make sure it is the correct extrema!!!
Other examples:
10 ft of wire are wrapped around a square and a circle. How much wire around each to maximize the area of the square and circle combined?
Two posts, 12 ft and 28ft, are 30 ft apart. Minimize the length of the rope that connects the top of each pole, if the wire is pulled tight and must touch the ground as well?