SOLUTION: Find two numbers whose difference is 14 and whose product is a minimum. Be sure to use "let statement".

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Question 196945: Find two numbers whose difference is 14 and whose product is a minimum. Be sure to use "let statement".
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the numbers be x and y
y+-+x+=+14
y+=+x+%2B+14
The product is x%2Ay
x%2Ay+=+x%2A%28x+%2B+14%29
x%2Ay+=+x%5E2+%2B+14x
The function f%28x%29+=+x%5E2+%2B+14x
Is a minimum when x+=+-b%2F%282a%29
a+=+1
b+=+14
x%5Bmin%5D+=+-14%2F2
x%5Bmin%5D+=+-7
y+=+x+%2B+14
y+=+-7+%2B+14
y+=+7
The numbers are 7 and -7
check:
The product is -49
If I change the numbers very slightly, what
happens to the product?
x+=+-6.9
y+=+x+%2B+14
y+=+-6.9+%2B+14
y+=+7.1
-6.9%2A7.1+=+-48.99
This gives me more confidence answer is right