question_answer

On the interval [0, 1], the function with \[{{\text{X}}^{\text{25}}}{{\left( \text{1-x} \right)}^{\text{75}}}\] takes its maximum value at the point

A) 0                                             

B) \[\frac{1}{4}\]

C) \[\frac{1}{2}\]                                   

D) \[\frac{1}{4}\]

Correct Answer: B

Solution :

Let \[=\frac{100000}{99}\approx 1010\] \[\Rightarrow \]  \[{{\text{C}}_{\text{6}}}{{\text{H}}_{\text{6}}}\left( \text{g} \right)\text{=}{{\text{p}}_{\text{1}}}\]        \[{{H}_{2}}\left( g \right)={{p}_{2}}mm\]        \[\therefore \]             Which shows that f?(x) is positive for \[{{p}_{1}}+{{p}_{2}}=60mm\] and f?(x) is negative for \[{{C}_{6}}{{H}_{6}}\left( g \right)=0\] Hence, f(x) attains maximum at \[{{H}_{2}}\left( g \right)={{p}_{2}}-3{{p}_{1}}\]