G Tewani Solutions for Chapter: Monotonicity and Maxima-Minima of Functions, Exercise 3: DPP

If $f\left(x\right)=|x-1|+|x-4|+|x-9|+\dots +|x-2500| \forall x\in R$, then set of all the values of $x$, where $f\left(x\right)$ has minimum values, is

Slope of tangent to the curve $y=2e^x\sin \left(\frac{\pi }{4}-\frac{x}{2}\right)\cos \left(\frac{\pi }{4}-\frac{x}{2}\right)$, is minimum at $x=$ $($where $0\le x\le 2\pi$$)$

The value of $a$ for which all extremum of function $f\left(x\right)=$$x^3-3a{x}^2+3\left(a^2-1\right)x+1$, lies in the interval $\left(-2, 4\right)$ is

If the function $f\left(x\right)=ax{e}^{-bx}$ has a local maximum at the point $(2,10)$, then

Let $f\left(x\right)=\frac{e^x}{1+x^2}$ and $g\left(x\right)=f^{\text{'}}\left(x\right)$, then

If $f^{\text{'}}\left(x\right)=(x-a{)}^{2010}(x-b{)}^{2009}$ and $a>b$, then

If $\underset{x\to a}{\lim }f\left(x\right)=\underset{x\to a}{\lim }\left[f\left(x\right)\right]$, where $[·]$ denotes the greatest integer function and $f\left(x\right)$ is a non-constant continuous function, then

Consider the function $f\left(x\right)={\log }_e(\sqrt{1-x^2}-x)$. Then, which of the following is/are true?