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Question

If f(x)=kx-cosx is monotonically increasing for all xR, then


A

K>1

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B

K<1

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C

K>1

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D

None of these

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Solution

The correct option is A

K>1


Explanation for correct option:

Find the value of k:

Given,

f(x)=kxcosx

Differentiated the given function with respect to x.

f'(x)=k+sinx

Since the function is monotonically increasing for all xR,f(x)>0, so

f'(π/2)>0k+sin(π/2)>0k+1>0k>-1

Hence, the correct option is A.


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