G Tewani Solutions for Chapter: Monotonicity and Maxima-Minima of Functions, Exercise 1: DPP

If $f\left(x\right)=\sin 2x-8(a+1)\sin x+\left(4a^2+8a-14\right)x$ increases for all $x\in R$ and has no critical points for all $x\in R$, then which of the following values of $a$ are not possible?

The minimum value of $k$ for which $f\left(x\right)=2e^x-k{e}^{-x}+\left(2k+1\right)x-3$ is monotonically increasing for all real $x$ is

If the function $f\left(x\right)=2\cot x+\left(2a+1\right){\log }_e\left(\mathrm{cosec}x\right)+\left(2-a\right)x$ is strictly decreasing in $\left(0, \frac{\pi }{2}\right),$ then range of '$a$' is:

Which of the following statement(s) is/are true?

Let $f: R\to R, f\left(x\right)=x+{\log }_e\left(1+x^2\right)$. Then,

Let $f\left(x\right)=x-\frac{1}{x}$, then which one of the following statement(s) is/are true?

Let $f\left(x\right)$ be an even function in $R.$ If $f\left(x\right)$ is monotonically increasing in $\left[2, 6\right]$, then

If $f\left(x\right)=\left\{\begin{array}{ll}-e^{-x}+k& , x\le 0\\ e^x+1& , 0<x<1\\ e{x}^2+\lambda & , x\ge 1\end{array}\right.$is one-one and monotonically increasing $\forall x\in R,$ then