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Show that for a ³ 1, f (x) = √3 sin x – cos x – 2ax + b is decreasing in R.
Show that for a ³ 1, f (x) = √3 sin x – cos x – 2ax + b is decreasing in R.
Application of Derivatives | Class 12 | Exercise 1 | Maths | NCERT Exemplar
Show that for a ³ 1, f (x) = √3 sin x – cos x – 2ax + b is decreasing in R.

ACCORDING TO QUES,

\[f~\left( x \right)\text{ }=\text{ }\surd 3\text{ }sin~x\text{ }~cos~x\text{ }~2ax\text{ }+\text{ }b,\text{ }a~{}^\text{3}\text{ }1\]

differentiating both sides w.r.t. x

WE HAVE

\[f~\left( x \right)\text{ }=\text{ }\surd 3\text{ }cos~x\text{ }+~sin~x\text{ }~2a\]

For increasing function, f’ (x) < 0

NCERT Exemplar Solutions Class 12 Mathematics Chapter 6 - 29

HENCE, function is decreasing in R.

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