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fezez5304
08.07.2019 •
Mathematics
Find the greatest possible value of the product xy, given that x and y are both positive and x + 2y = 30
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Ответ:
The maximum value of the product x*y is 112.5
Step-by-step explanation:
We have that x + 2y = 30
so we can isolate one of the variables and get:
x = 30 - 2y
now, the product of x*y can be written as:
x*y = (30 - 2y)*y = 30y - 2y^2
now, we want to find the maximum of 30y - 2y^2
because the leading coeficient is negative (-2), we know that the hands of the quadratic function will go downwards, so the zero of the derivate of this quadratic equation will give us the value where the equation has a maximum:
f(y) = -2*y^2 + 30*y
f'(y) = -4*y + 30 = 0
y = -30/4 = 7.5
So the maximum value is:
f(7.5) = -2*7.5^2 + 30*7.5 = 112.5
Ответ: