SOLUTION: 2. Find two numbers whose difference is 14 and whose product is a minimum.

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Question 175741: 2. Find two numbers whose difference is 14 and whose product is a minimum.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let's call your two numbers, A and B.
"difference is 14"
1.A-B=14
"product is a minimum"
2.f=A%2AB
We want to minimize f.
First, substitute for A and make f only a function of B.
1.A-B=14
A=14%2BB
f%28B%29=%2814%2AB%29%2AB=14B%2BB%5E2
To minimize, take the derivative wrt B and set it equal to 0.
df%2FdB=14%2B2B=0
B=-7
Then from 1,
A=14%2BB
A=14-7
A=7