What is the minimum product of two numbers whose difference is 22? What numbers yield this product?
FYI i asked my teacher and she didn't quite explain it the way i hoped so i was hoping someone could explain it better ?
Hello, diehardmath4!
What is the minimum product of two numbers whose difference is 22?
What numbers yield this product?
Let = the larger number.
Let = the smaller number.
Their difference is 22: . .[1]
Their product is: . .[2]
Substitute [1] into [2]: .
This is an up-opening parabola; its minimum is at its vertex.
The vertex is at: .
Substitute into [1]: .
The minimum product is: .