SOLUTION: One number is 10 greater than the other number. Find the two numbers such that their product is a minimum. What is the product?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: One number is 10 greater than the other number. Find the two numbers such that their product is a minimum. What is the product?      Log On


   

Question 118651: One number is 10 greater than the other number. Find the two numbers such that their product is a minimum. What is the product?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let N be the first number.
Then N+10 is the second number.
Their product is N(N+10).
P=N%28N%2B10%29
P=N%5E2%2B10N
To find a minimum, set the derivative of P with respect to N equal to zero.
dP%2FdN=2N%2B10
Now set it equal to zero.
dP%2FdN=2N%2B10=0
2N=-10
N=-5
N%2B10=5
Graphically, the product function N(N+10) shows the same result.
Here x=N and y=N(N+10).
+graph%28+300%2C+300%2C+-10%2C+10%2C+-100%2C+100%2C+x%5E2%2B10x%29+
The first number is -5.
The second number is 5.
Their product is -25.