Maxima and MinimaHard
Question
On the interval [0, 1] the function x25 (1 - x)75 takes its maximum value at the point -
Options
A.0
B.13
C.1/2
D.1/4
Solution
f(x) = x25 (1- x)75
f′(x) = 25.x24 (1- x)75 - 75.(1- x)74. x25
= 25. x24 (1- x)74{1- x - 3x}
= 25x24 (1- x)74 (1 - 4x)
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