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Question

The maximum value of e2+3cosx+sinx is


A

e2

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B

e2-3

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C

e4

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D

1

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Solution

The correct option is C

e4


Explanation for correct option:

Let, y=e2+3cosx+sinx

ex is an increasing function,so y will attain maximum value when 2+3cosx+sinx will be maximum.

We know, -a2+b2asinx+bcosxa2+b2

So, maximum value of 2+3cosx+sinx is 2+32+12=4

Hence, maximum value of y is e4

Hence the correct option is option C.


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