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Question

The value of a in order that f(x)=sinx-cosx-ax+b decreases for all real value of x is given by


A

a2

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B

a<2

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C

a1

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D

a<1

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Solution

The correct option is A

a2


Explanation for the correct option:

Find the value of a:

A function f(x)=sinx-cosx-ax+b is given.

It is also given that the given function is a strictly decreasing function.

We know that, if a function is a decreasing function, then the derivative of the function is less than zero.

Therefore, f'x<0.

cosx+sinx-a<0212cosx+12sinx-a<0a>212cosx+12sinxa>2sinπ4+x

So, for strictly decreasing function a2.

Therefore, The value of a in order that f(x)=sinx-cosx-ax+b decreases for all real value of x is given by a2.

Hence, option (A), a2 is the correct answer.


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