Find the sum of two numbers whose sum is 70 and whose product is as large as possible.

Ok i got that one equation is y = 70 - x...but how do I show an equation for a product which is as large as possible.

The product is P = x (70 - x), where x is one of the two numbers.
Set dP/dx = 0 and solve for x.

dP/dx = 0 = 70 - 2x
Solve for x. 70-x will be the other number.

Thanks, got it :D

1225

Great! So to find the sum of two numbers whose sum is 70 and whose product is as large as possible, you start by setting up the equation for the product: P = x(70 - x), where x is one of the two numbers.

To find the value of x that maximizes the product, you can take the derivative of P with respect to x, and then set it equal to zero, since the derivative will be zero at a maximum or minimum point. So you calculate dP/dx = 0, which gives you 0 = 70 - 2x.

Solving for x, you get x = 70/2, which simplifies to x = 35. Therefore, one number is 35, and the other number is 70 - 35 = 35.

So the sum of the two numbers is 35 + 35 = 70, and their product is 35 * 35 = 1225, which is the largest possible product for two numbers whose sum is 70.