(C) Given the function $f(x) = |x^2 - x|$.For $x$ near $2$,$x^2 - x$ is positive because $2^2 - 2 = 2 > 0$.Since $x^2 - x > 0$ in an open interval aro

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

(C) Given the function $f(x) = |x^2 - x|$.For $x$ near $2$,$x^2 - x$ is positive because $2^2 - 2 = 2 > 0$.Since $x^2 - x > 0$ in an open interval around $x = 2$,we can write $f(x) = x^2 - x$.Now,find the derivative $f'(x) = \frac{d}{dx}(x^2 - x) = 2x - 1$.Evaluating at $x = 2$,we get $f'(2) = 2(2) - 1 = 4 - 1 = 3$.

Class 12 Mathematics Continuity and Differentiation Derivative at a point, Standard differentiation

Easy

The derivative of $f(x) = |x^2 - x|$ at $x = 2$ is

A
$-3$
B
$0$
C
$3$
D
Not defined

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Mathematics Questions

Chapter

Continuity and Differentiation

Subtopic

Derivative at a point, Standard differentiation

If $y=(1+x)(1+x^2)(1+x^4) \dots (1+x^{2^n})$, then $\left(\frac{dy}{dx}\right)_{x=0}$ is equal to

MediumAP EAMCET 2011

View Solution

$A$ possible positive value of '$a$',for which $f^{\prime}(x)=0$ has equal roots,is

MediumAP EAMCET 2023

View Solution

Differentiate the function with respect to $x$: $\sin^{3} x + \cos^{6} x$

Medium

View Solution

Let $f$ be differentiable at $x = 0$ and $f'(0) = 1$. Then $\lim_{h \to 0} \frac{f(h) - f(-2h)}{h} = $

View Solution

If $f: R \rightarrow R$ is an even function having derivatives of all orders, then which of the following is an odd function?

EasyAP EAMCET 2004

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 derivative of $f(x) = |x^2 - x|$ at $x = 2$ is

Similar Questions

If $y=(1+x)(1+x^2)(1+x^4) \dots (1+x^{2^n})$, then $\left(\frac{dy}{dx}\right)_{x=0}$ is equal to

$A$ possible positive value of '$a$',for which $f^{\prime}(x)=0$ has equal roots,is

Differentiate the function with respect to $x$: $\sin^{3} x + \cos^{6} x$

Let $f$ be differentiable at $x = 0$ and $f'(0) = 1$. Then $\lim_{h \to 0} \frac{f(h) - f(-2h)}{h} = $

If $f: R \rightarrow R$ is an even function having derivatives of all orders, then which of the following is an odd function?

Vedclass Test Series

Exam Paper Generator

Online Exam Module