Find the maximum product of two numbers whose sum euqals 124. Let's call the numbers "x" and "y". Also, what are those two numbers?
x+y=124 or x=124-y dx=dy
A= xy = (124-y)y
dA/dy=0=124-2y
y=62 then solve for x
whew, great! that's what I got, too :-)
Thank You! I have one more, if you're up for it
To find the maximum product of two numbers whose sum is 124, we can follow these steps:
1. Write the equation: x + y = 124, where x and y are the two numbers.
2. Solve for one variable in terms of the other: Let's solve for y. Subtract x from both sides of the equation: y = 124 - x.
3. Formulate the product: The product P is given by P = x * y.
4. Substitute the value of y in terms of x into the product equation: P = x * (124 - x).
5. Simplify the product equation: P = 124x - x^2.
6. This equation represents a quadratic function. To find the maximum product, we need to find the vertex of the quadratic equation, which will give us the maximum value.
7. The vertex of a quadratic equation in the form of ax^2 + bx + c can be found using the formula: x = -b / (2a). In our case, a = -1, b = 124, and c = 0, so we have x = -124 / (2 * -1) = 62.
8. To find the value of y, substitute the value of x into one of the original equations. In this case, we can use the equation x + y = 124: 62 + y = 124. Solving for y gives us y = 62.
Therefore, the two numbers that yield the maximum product are x = 62 and y = 62, which sum up to 124.