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  • Please solve RD Sharma class 12 chapter 16 Increasing and Decreasing Function Excercise Very Short Answer type Question 14 Maths Textbook Solution.

Please solve RD Sharma class 12 chapter 16 Increasing and Decreasing Function Excercise Very Short Answer type Question 14 Maths Textbook Solution.

Answers (1)

Answer:

The set of values of  a  for which  f(x)  is strictly increasing is a\epsilon (-\infty ,-1]\cup [1,\infty )

Hint:

If  f(x)  is increasing, then f'(x)>0

Given:

                f(x)=\cos x+a^{2}x+b

Explanation:

It is given that,

                f(x)=\cos x+a^{2}x+b

\Rightarrow         f'(x)=-\sin x+a^{2}                                                                                                                     

\therefore         f'(x)>0    as   f(x)  is increasing

\Rightarrow         -\sin x+a^{2}>0

\Rightarrow         a^{2}>\sin x

\Rightarrow         a\epsilon (-\infty ,-1]\cup [1,\infty )                                                                                                                                    

The set of values of a for which f(x)is strictly increasing is  a\epsilon (-\infty ,-1]\cup [1,\infty )

 

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