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

Important Questions on Application of Derivatives

HARD

Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 40

Let $f\left(x\right)=\frac{40}{3x^4+8x^3-18x^2+60}$. Which of the following statement(s) about $f\left(x\right)$ is (are) correct ?

HARD

Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 41

Let $f:R\to (0,\infty )$ and $g:R\to R$ be twice differentiable functions such that $f^{"}$ and $g^{"}$ are continuous functions on $R$. Suppose $f^{\text{'}}\left(2\right)=g\left(2\right)=0,f^{"}\left(2\right)\ne 0$ and $g^{\text{'}}\left(2\right)\ne 0$, If $\underset{x\to 2}{\lim }\frac{f\left(x\right)g\left(x\right)}{f^{\text{'}}\left(x\right)g^{\text{'}}\left(x\right)}=1$, then

HARD

Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 42

The function $\frac{\sin (\mathrm{x}+\mathrm{a})}{\sin (\mathrm{x}+\mathrm{b})}$ has no maxima or minima, if

HARD

Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 48

The number of the tangents that can be drawn to the curve $y^2-2x^3-4y+8=0$ from the point $(1,2)$, is

HARD

Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 49

If the area enclosed by normal to the curve $y=(1+x{)}^y+{\sin }^{-1}\left({\sin }^{2}x\right)$ at $x=0$ with coordinate axes (in sq. units) is $k$, then the value of $2k$ is

HARD

Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 50

If the point of intersection of the tangents drawn to the curve $x^{2}y=1-y$ at the points where it is intersected by the curve $x y=1-y$, is $(a, b)$, then $a+b$ is