Applications of Cubic Functions

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Presentation transcript:

Applications of Cubic Functions

Volume of a Open Box. Suppose you are trying to make an open-top box out of a piece of cardboard that is 20 inches by 16 inches. You are to cut the same size square from each corner. Write a function to represent the volume of this box. 20 x 20 - 2x 16 - 2x 16

V=lwh 20 - 2x ? x 16 - 2x 20 - 2x

Formula for the Volume of a Box The final answer for the volume will ALWAYS have the term :

Write the formula for the volume of our box: Step 1: Multiply the two binomials together Step 2: Multiply by x 20 -2x 16 320 -40x -32x 4x2

What is the maximum volume? What is the possible domain for this box? What is the greatest possible value that we can cut out for x? 0 < X < 8 (Half of the length of the smallest side) SO, Xmin = 0 and Xmax = 8; ZOOM 0 Do you want x or y? Y!!! 420 cubic inches

What size square should be cut from each corner to realize the maximum volume? What do you want now? X!! 2.9 inches

Y!! Let y = 300; find the intersection What size square should you cut from each corner to realize a volume of 300 cubic inches? What do you know: x or y? Y!! Let y = 300; find the intersection 1.3 inches or 5 inches

What is the volume if a square with side 2 inches is cut from each corner? What do you know; x or y? X!!! Go to table; let x = 2 384 Cubic inches