Chapter 4, Problem 18PS

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Chapter
Section

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

# Minimum Length A legal-sized sheet of paper (8.5 inches by 14 inches) is folded so that comer P touches the opposite14-inch edge at R (see figure). ( N o t e : P Q = C 2 − x 2 . ) (a) Show that C 2 = 2 x 3 2 x − 8.5 (b) What is the domain of C?(c) Determine the x-value that minimizes C.(d) Determine the minimum length C.

(a)

To determine

To prove: The expression C2=2x32x8.5 is true.

Explanation

Given:

The paper is folded such that P touches R.

Proof:

The situation can be illustrated as:

From the provide figure:

PQ2+x2=C2PQ=C2âˆ’x2TR2+(8.5âˆ’x)2=x2TR=17xâˆ’8.52

Also,

(PQâˆ’TR)2+(8.5)2=PQ22(PQ)(TR)=TR2+8

(b)

To determine
The domain of C where C2=2x32x8.5.

(c)

To determine

To calculate: The value of x that minimizes C where C(x)=2x22x8.5.

(d)

To determine

To calculate: The minimum value of C if C(x)=2x22x8.5

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