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Q.

On the interval [0, 1] the function $x^{25} (1 - x)^{75}$ takes its maximum value at the point

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a

0

b

$\frac{1}{2}$

c

$\frac{1}{4}$

d

$\frac{1}{3}$

answer is B.

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Detailed Solution

$\frac{d y}{d x} = 0 25 x^{24} {(1 - x)}^{75} - 75 x^{25} {(1 - x)}^{74} = 0 \Rightarrow x = \frac{1}{4} \in (0, 1) M a x = m a x \{f (0), f (1), f (\frac{1}{4})\}$

$∴$ Max. value of y occurs at $x = \frac{1}{4}$

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