let y=2x-8. What is the minimum value of the product xy?
I'm not really sure how to do this...
I tried taking x*(2x-8), and the min is 0. but then i wanted to see if it was the same when solving for x, and i got a min of -8. How do i do this problem?
thanks, but i found which step i was missing.
thanks, but i found which step i was missing.
To find the minimum value of the product xy, you can follow these steps:
1. The given equation is y = 2x - 8.
2. Rewrite the equation in terms of x: xy = x(2x - 8).
3. Simplify the equation: xy = 2x^2 - 8x.
4. This equation represents a quadratic function in the form of ax^2 + bx + c, where a = 2, b = -8, and c = 0.
5. To find the minimum value of the quadratic function, we need to find the x-coordinate of the vertex.
6. The x-coordinate of the vertex is given by x = -b / (2a).
In this case, x = -(-8) / (2(2)) = 8 / 4 = 2.
7. Plug x = 2 back into the original equation to find the minimum value:
y = 2(2) - 8 = 4 - 8 = -4.
8. So, the minimum value of the product xy is -4.
I hope this helps! Let me know if you have any further questions.