Dla jakich liczb x i y ich iloczyn przyjmuje największą wartość, jeżeli suma tych liczb jest równa 100?
x + y = 100
y = 100 - x
x * y = x * (100 - x) = -x( x -100) = -x² + 100x
a = -1 b = 100 c = 0
p = -b/2a = -100/(-2) = 50
q = f(p) = -50² + 100 * 50 = -2500 + 5000 = 2500
f max (50) = 2 500
x = 50
y = 100 - x = 100 - 50 = 50
odp. x = 50 y = 50
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x + y = 100
y = 100 - x
x * y = x * (100 - x) = -x( x -100) = -x² + 100x
a = -1 b = 100 c = 0
p = -b/2a = -100/(-2) = 50
q = f(p) = -50² + 100 * 50 = -2500 + 5000 = 2500
f max (50) = 2 500
x = 50
y = 100 - x = 100 - 50 = 50
odp. x = 50 y = 50