What is the largest possible product of two negative number whose sum is 1?
two negative numbers can not add to +1
oh I'm sorry the problem actually say two non-negative numbers I misread the problem
x(1-x)=product
dProduct/dx=1-x + x(-1)=0
-2x=-1
x=1/2
other number is 1/2
largest product is 1/4
To find the largest possible product of two negative numbers whose sum is 1, we can start by understanding the given conditions:
1. We need to find two negative numbers.
2. The sum of these two negative numbers should be 1.
Let's assume the two negative numbers are x and y, where x and y are both less than 0.
According to the given conditions, we have the equation:
x + y = 1
To maximize the product, we should make both x and y as negative as possible. Since the sum is positive, one number should be close to 0 (approaching 0 from the negative side), and the other should be as negative as possible.
By intuition, let's consider x = -0.1 and y = -0.9. This satisfies the equation: -0.1 + (-0.9) = 1.
Now, let's calculate the product of x and y:
Product = x * y = (-0.1) * (-0.9) = 0.09
So, the largest possible product of two negative numbers whose sum is 1 is 0.09.
In general, to solve similar problems, start by understanding the given conditions and then optimize the variables accordingly.