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# powerpoint - Applications of the Derivative Questions of...

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Applications of the Derivative Questions of Optimization

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Optimization Nutshell version: to find the maximum or minimum of a function that models a situation. How many items should you sell to maximize profit? How many items should you produce to minimize cost? What dimensions should you use for a package in order to maximize volume and minimize surface area?
Maximize P = xy with x + y = 10 First, use the constraint to solve for one of the variables and make a substitution in the objective function. Second, take the derivative of the objective function and find critical points. Third, determine where the maximum is. Fourth, find the maximum value of the function. P is called the objective function and x + y = 10 is called a constraint

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P = xy with x + y = 10 x + ψ=10 ψ=-ξ+10 P = ξψ Π=ξ(-ξ+1029 = -ξ 2 + 10ξ 1. 2. P ' = -2ξ + 10 Critical Points: P’ is linear, so it’s always defined. P’ = 0 when x = 5 5 P '(4) = 2 0 P '(6) = -2 < 0 + - P has a maximum at x = 5. 3.
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powerpoint - Applications of the Derivative Questions of...

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