   Chapter 3.7, Problem 73E

Chapter
Section
Textbook Problem

# The upper right-hand corner of a piece of paper, 12 in. by 8 in., as in the figure, is folded over to the bottom edge. How would you fold it so as to minimize the length of the fold? In other words, how would you choose x to minimize y? To determine

To choose:

The value of x to minimize y

Explanation

1) Concept:

If f''x>0 if and only if fx is the absolute minimum value, where f'x=0

2) Calculation:

The upper right hand corner of a piece of paper, 12 in. by 8 in.

We would minimize the length of the fold that means

fx=y2

By using Pythagorean Theorem In DCB

y2=z2+x2

So, fx=z2+x2

By using Pythagorean Theorem

AC=x2-8-x2

AC=x2-64+16x-x2

AC=16x-4

AC=4x-4

Since CDE ~ BCA, we have

zx=84x-4

z=8x4x-4

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