   Chapter 3.7, Problem 2E

Chapter
Section
Textbook Problem

# Find two numbers whose difference is 100 and whose product is a minimum.

To determine

To find:

Two numbers whose difference is 100 and whose product is a minimum

Explanation

1) Concept:

Using the second derivative test we can say that the product is minimum

Second derivative test: suppose f''is continuous near c

a) If f'c=0 and f''c>0 then f has a local minimum at  c

b) If f'c=0 and f''c<0 then f has a local maximum at  c

2) Calculation:

Let two numbers m and nbe such that their difference is 100

I.e. m-n=100

Rewrite min terms of nas m=n+100

Let product P=n·(n+100)

Simplify

P=n2+100n

Differentiate Pusing the pow

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