Answer:
If one number is x, the other is (96 - x)...since if you add those two together, you will get 96..and the product is x(96 - x) = 96x - x^2
Since this is a quadratic function (x to the power of 2), it is a parabola. More specifically, it is a parabola opening downwards, because there is a negative in front of the x squared. Because it downward facing the maximum value of x is going to be where the vertex is. The x value of the vertex can be found by taking the negative of b (which is the number in front of teh x) over a squared (which is the number in front of the x squared which in this case is 1)
So x = -96 / 2(-1) = -96/-2 = 48
Since as we first stated one number is x, the first number is 48
The second number will be 48, because we stated the second number to be 96-x
Therefore 48 times 48 will give you the maximum product 2304.
Hope This Helps!!!!!!!!!!!!!!
Answer:
3,600
Step-by-step explanation:
x + y = 120
y = 120 - x
Product "P"
P = x × y = x(120-x) = 120x - x²
P = -(x² - 20x)
= -(x² - 2(x)(60) + 60² - 60²)
= -(x - 60)² + 3600
Max value is 3,600
