(C) The graph represents the function $f(x) = |x-1|$.At $x=1$,the graph is continuous because there is no break in the curve.However,at $x=1$,there is

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Continuous but not differentiable at $x=1$

(C) The graph represents the function $f(x) = |x-1|$.At $x=1$,the graph is continuous because there is no break in the curve.However,at $x=1$,there is a sharp corner (or cusp),which means the left-hand derivative and right-hand derivative are not equal.Specifically,the left-hand derivative is $-1$ and the right-hand derivative is $1$.Therefore,the function is continuous but not differentiable at $x=1$.

Class 12 Mathematics Continuity and Differentiation Differentiability

Difficult

The function represented by the following graph is,

KCET 2014 All KCET

A
Differentiable but not continuous at $x=1$
B
Neither continuous nor differentiable at $x=1$
C
Continuous but not differentiable at $x=1$
D
Continuous and differentiable at $x=1$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Mathematics Questions

Chapter

Continuity and Differentiation

Subtopic

Differentiability

Previous Year

KCET 2014 Paper All KCET years →

The function $f(x) = a \sin |x| + b e^{|x|}$ is differentiable at $x = 0$ when

MediumWBJEE 2014

View Solution

If $f(x) = \begin{cases} \frac{x-1}{2x^2-7x+5}, & \text{for } x \neq 1 \\ -\frac{1}{3}, & \text{for } x=1 \end{cases}$,then $f^{\prime}(1)$ is equal to:

DifficultAP EAMCET 2003

View Solution

Let $f(x) = \begin{cases} a \sin(x + b) & x \ge 0 \\ 6x^7 - x + 1 & x < 0 \end{cases}$ be differentiable for all real $x$. If $a \in \mathbb{R}$ and $b \in [0, 2\pi]$,then the number of ordered pairs $(a, b)$ is:

View Solution

Let $a \in Z$ and $[t]$ be the greatest integer $\leq t$. Then the number of points,where the function $f(x) = [a + 13 \sin x], x \in (0, \pi)$ is not differentiable,is $........$.

JEE MAIN 2023

View Solution

Let $S = \{t \in R : f(x) = |x-\pi|(e^{|x|}-1)\sin|x| \text{ is not differentiable at } t\}$. Then the set $S$ is equal to:

DifficultJEE MAIN 2018

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

The function represented by the following graph is,

Similar Questions

The function $f(x) = a \sin |x| + b e^{|x|}$ is differentiable at $x = 0$ when

If $f(x) = \begin{cases} \frac{x-1}{2x^2-7x+5}, & \text{for } x \neq 1 \\ -\frac{1}{3}, & \text{for } x=1 \end{cases}$,then $f^{\prime}(1)$ is equal to:

Let $f(x) = \begin{cases} a \sin(x + b) & x \ge 0 \\ 6x^7 - x + 1 & x < 0 \end{cases}$ be differentiable for all real $x$. If $a \in \mathbb{R}$ and $b \in [0, 2\pi]$,then the number of ordered pairs $(a, b)$ is:

Let $a \in Z$ and $[t]$ be the greatest integer $\leq t$. Then the number of points,where the function $f(x) = [a + 13 \sin x], x \in (0, \pi)$ is not differentiable,is $........$.

Let $S = \{t \in R : f(x) = |x-\pi|(e^{|x|}-1)\sin|x| \text{ is not differentiable at } t\}$. Then the set $S$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module