The function $f\left(x\right)={\sin }^{4}x+{\cos }^{4}x$ increases, if

Important Questions on Application of Derivatives

EASY

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 1 - Application of Derivatives>Level 1>Q 19

The interval of monotonicity of the function, $f\left(x\right)=\frac{x}{{\log }_{e}x}$ is

MEDIUM

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 1 - Application of Derivatives>Level 1>Q 20

Function $f\left(x\right)=x^4-\frac{x^3}{3}$ is

MEDIUM

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 1 - Application of Derivatives>Level 1>Q 21

For which interval the given function $f\left(x\right)=-2x^3-9x^2-12x+1$ is decreasing?

MEDIUM

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 1 - Application of Derivatives>Level 1>Q 22

The function $f\left(x\right)=\frac{\ln \left(\pi +x\right)}{\ln \left(e+x\right)}$ is

MEDIUM

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 1 - Application of Derivatives>Level 1>Q 23

The function $f\left(x\right)=x^{\frac{1}{x}}$ is increasing in the interval

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 1 - Application of Derivatives>Level 1>Q 24

If $f\left(x\right)=x^3+a{x}^2+bx-5{\cos }^{2}x$ is an increasing function for all real values of $x,$ then $a,$ and $b$ satisfy the condition

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 1 - Application of Derivatives>Level 1>Q 25

If $f\left(x\right)=\left\{\begin{array}{cc}3+\left|x-k\right|& , \mathrm{f}\mathrm{o}\mathrm{r} x\le k\\ a^2-2+\frac{\sin \left(x-k\right)}{x-k}& , \mathrm{f}\mathrm{o}\mathrm{r} x>k\end{array}\right.$ has minimum at $x=k,$ then

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 1 - Application of Derivatives>Level 1>Q 26

Let $f\left(x\right)=x^{n+1}+a·x^n$, where $a$ and $n$ are positive real number. Then, $x=0$ is a point of: