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Priscila Andrade 12/October/2001 Calculus period 3

Optimization. Priscila Andrade 12/October/2001 Calculus period 3. Here's our Problem.

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Priscila Andrade 12/October/2001 Calculus period 3

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  1. Optimization Priscila Andrade 12/October/2001 Calculus period 3

  2. Here's our Problem An open rectangular box is to be made from a piece of cardboard 8 inches wide and 15 inches long by cutting squares from the corners and folding up the sides. Find the dimensions of the box of the largest possible volume.

  3. What do we know? x x Width=8 in x x Length=15 in. AND…….

  4. What else do we know? Height of the box= X Width=8-2x Length of the box= 15-2x

  5. Our equations are... Primary Function L W H Volume= (15-2x)(8-2x)(x) =120x-46x2+4x3 Volume=LWH L=15-2x W=8-2x H=X substitute Find the Derivative by using the power rule V’=120-92x+12x2

  6. Finding the Maxima... Derivative V’=120-92x+12x2 set derivative = to 0 and solve for X 0=(6-x)(5-3x) X=6 or X=5/3 Sign Table (6-x) + + - (5-3x) + - - 6 5/3 The Maxima is

  7. Finding more values 35/3 X=5/3 L=15-2x=15-2(5/3)=35/3 W=8-2x=8-2(5/3)=14/3 H=X=5/3 5/3 14/3

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