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Question

On the interval 0,1, the function x25(1-x75) takes its maximum value at the point


A

0

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B

14

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C

12

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D

13

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Solution

The correct option is B

14


Explanation for the correct answer:

Finding the maximum value of the function:

Given,
f(x)=x251-x75
Differentiating,

f'(x)=25x24+1-x75+75x251-x74dxadx=axa-1=x241-x7425(1-x)-75x=25x241-x741-x-3x=25x241-x741-4x

So values of x are,

25x24=0x=241-x74=01-x=0x=11-4x=0-4x=-1x=14

Therefore,

x=0,1,14

Hence, x=14is the maximum value.

Therefore, the correct answer is option (B).


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