Respuesta :
The biggest possible real number = 60 ÷ 2 = 30
30 + 30 = 60
Largest Product = 30 x 30 = 900
Answer: The two numbers are 30 and 30.
30 + 30 = 60
Largest Product = 30 x 30 = 900
Answer: The two numbers are 30 and 30.
The two non negative real numbers with a sum of 60 that have the largest possible product are; 30 and 30.
Let the two numbers be x and y.
Thus, if their sum is 60, then we have;
x + y = 60
y = 60 - x
Their product will be;
P = xy
Putting (60 - x) for y in the product equation we have;
P = (60 - x)x
P = 60x - x²
Since the product is maximum, let us find the derivative;
P'(x) = 60 - 2x
At P'(x) = 0, we have;
60 - 2x = 0
2x = 60
x = 60/2
x = 30
Thus; y = 60 - 30
y = 30
Thus, the two non negative real numbers are 30 and 30.
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