R D Sharma Solutions for Chapter: Increasing and Decreasing Functions, Exercise 1: MULTIPLE CHOICE QUESTIONS (MCQs)

What are the values of $a$ for which $f\left(x\right)=a^x$ is decreasing on $R$?

Find $a$ for which $f\left(x\right)=a\left(x+\sin x\right)+a$ is increasing on $R$.

Find the values of $a$ for which the function $f\left(x\right) =\sin x-ax+4$ is increasing function on $R$.

Find the set of values of $b$ for which $f\left(x\right)=b\left(x+\cos x\right)+4$ is decreasing on $R$.

Find the set of values of $a$ for which $f\left(x\right)=x+\cos x+ax+b$ is increasing on $R$.

Write the set of values of $k$ for which $f\left(x\right)=kx-\sin x$ is increasing on $R$. 

Write the set of values of $a$ for which the function $f\left(x\right)=ax+b$ is decreasing for all $x\in R$.

Write the interval in which $f\left(x\right)=\sin x+\cos x,x\in \left[0,\frac{\mathrm{\pi }}{2}\right]$ is increasing.