Найдите область определения и область значений функции, заданной формулой:
y=[tex] \sqrt{x-x^2} [/tex]
y=[tex] \sqrt{x-x^2} [/tex]
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D(y)x-x²≥0
x(1-x)≥0
x=0 x=1
_ + _
-----[0]------------[1]------------
x∈[0;1]
E(y)
y`=(1-2x)/2√(x-x²)=0
1-2x=0
x=1/2
+ -
[0]----------[1/2]--------------[1]
max
y(1/2)=√(1/2-1/4)=√(1/4)=1/2
y∈[0;1/2]