VITEEE 2015 Paper

Let f (x) = x25(1−x)75 , x ∊ [0 , 1]
⇒ f ' (x) = 25x24(1−x)75−75x25 (1−x)74
= 25x24(1−x)74 {(1 - x) - 3x}
= 25x24(1−x)74 (1 - 4x)
We can see that f’(x) is positive for x <

1

4

and f ' (x) is negative for x >

1

4

Hence,f (x) attains maximum at x =

1

4