Which of the following statements are true:

Important Questions on Application of Derivatives

HARD

Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 32

A function $f\left(x\right)=\frac{x^2-3x+2}{x^2+2x-3}$ is

HARD

Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 33

For the function $f\left(x\right)=x\cos \frac{1}{x}, x\ge 1$

HARD

Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 34

A function $y=f\left(x\right)$ is given by $x=\frac{1}{1+t^2} \& y=\frac{1}{t\left(1+t^2\right)}$ for all $t>0$ then $f$ is

HARD

Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 35

Suppose $f^{\text{'}}\left(x\right)$ exists for each $x$ and $h\left(x\right)=f\left(x\right)-{\left(f\left(x\right)\right)}^2+{\left(f\left(x\right)\right)}^3 \forall x\in R$, then

HARD

Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 36

Let $f\left(x\right)=\mathrm{l}\mathrm{n}\left(2x-x^2\right)+\mathrm{s}\mathrm{i}\mathrm{n}\frac{\mathrm{\pi }x}{2}$. Then,

HARD

Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 37

Let $f\left(x\right)=ab\mathrm{s}\mathrm{i}\mathrm{n}x+b\sqrt{1-a^2}\mathrm{c}\mathrm{o}\mathrm{s}x+c$, where $\left|a\right|<1, b>0,$ then

HARD

Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 38

$f\left(x\right)=\sqrt{x-1}+\sqrt{2-x}$ and $g\left(x\right)=x^2+bx+c$ are two given functions such that $f\left(x\right)$ and $g\left(x\right)$ attain their maximum and minimum values respectively for same value of $x$, then

HARD

Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 39

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