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

Important Questions on Monotonicity and Maxima-Minima of Functions

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 6 - Monotonicity and Maxima-Minima of Functions>DPP>Q 14

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

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 6 - Monotonicity and Maxima-Minima of Functions>DPP>Q 15

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

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 6 - Monotonicity and Maxima-Minima of Functions>DPP>Q 1

If $f\left(x\right)=\left\{\begin{array}{cl}{x}^3(1-x),& x\le 0\\ x{\log }_{e}x+3x,& x>0\end{array}\right.$, then which of the following is not true

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 6 - Monotonicity and Maxima-Minima of Functions>DPP>Q 2

The coordinates of the point on the curve $x^3=y(x-a{)}^2$, where the ordinate is minimum is

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 6 - Monotonicity and Maxima-Minima of Functions>DPP>Q 3

The fraction exceeding its $p^{\mathrm{th}}$ power by the greatest number possible, where $p\ge 2$, is:

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 6 - Monotonicity and Maxima-Minima of Functions>DPP>Q 4

If $f\left(x\right)=\left\{\begin{array}{ll}x,& 0\le x\le 1\\ 2-e^{x-1},& 1<x\le 2\\ x-e,& 2<x\le 3\end{array}\right\}$ and $g^{\text{'}}\left(x\right)=f\left(x\right)$, $x\in [1, 3]$, then:

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 6 - Monotonicity and Maxima-Minima of Functions>DPP>Q 5

If $g\left(x\right)=\max \left(y^2-xy\right)$ (where $0\le y\le 1$), then the minimum value of $g\left(x\right)$ (for real $x$) is:

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 6 - Monotonicity and Maxima-Minima of Functions>DPP>Q 6

If $a, b\in R$ distinct numbers satisfying $\left|a-1\right|+\left|b-1\right|=\left|a\right|+\left|b\right|=\left|a+1\right|+\left|b+1\right|,$ then the minimum value of $\left|a-b\right|$ is: