Answered: Find C'(x) and C''(x)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.6: Regression And Median-fit Lines

Problem 20PFA

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Question

Consider a storage box with a square base. Let the square base measure x cm by x cm, and let y represent the height of the box in centimeters. Let V represent the volume of the box, measured in cubic centimeters. Write an equation for V in terms of x and y.

V =

Let C represent the cost of the box, measured in dollars. The volume of the box must be 70 cubic centimeters. Further, the top and bottom of the box cost $0.20 per square centimeter and the sides cost $0.10 per square centimeter. Use this information to write an equation for C in terms of x.

C(x) =

Find

C'(x)

and

C''(x).

Find the dimensions (in cm) that will minimize cost. (Round your answers to two decimal places.)

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