The set of points where f(x) = frac{4x}{5 + 6 | vedclass

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

Question

(C) Given $f(x) = \frac{4x}{5 + 6|x|}$.We can define $f(x)$ as:$f(x) = \begin{cases} \frac{4x}{5 - 6x}, & x < 0 \ \frac{4x}{5 + 6x}, & x \geq 0 \end{

Vedclass · Accepted Answer

$( - \infty, \infty)$

Vedclass · Answer

(C) Given $f(x) = \frac{4x}{5 + 6|x|}$.We can define $f(x)$ as:$f(x) = \begin{cases} \frac{4x}{5 - 6x}, & x To check differentiability at $x = 0$,we find the left-hand derivative $(LHD)$ and right-hand derivative $(RHD)$:$f'(x) = \begin{cases} \frac{4(5 - 6x) - 4x(-6)}{(5 - 6x)^2} = \frac{20}{(5 - 6x)^2}, & x  0 \end{cases}$Now,$f'(0^-) = \lim_{x 	o 0^-} \frac{20}{(5 - 6x)^2} = \frac{20}{25} = \frac{4}{5}$.And $f'(0^+) = \lim_{x 	o 0^+} \frac{20}{(5 + 6x)^2} = \frac{20}{25} = \frac{4}{5}$.Since $f'(0^-) = f'(0^+) = \frac{4}{5}$,the function is differentiable at $x = 0$.Since the function is a rational function with a non-zero denominator for all $x \in \mathbb{R}$,it is differentiable everywhere.Thus,the set of points is $( - \infty, \infty)$.

The set of points where $f(x) = \frac{4x}{5 + 6|x|}$ is differentiable is:

Similar Questions

Which of the following statements is not true?

The number of points,at which the function $f(x) = |2x+1| - 3|x+2| + |x^2+x-2|$,$x \in R$ is not differentiable,is ............

The function $y = \sin^{-1}\left(\frac{2x}{1 + x^2}\right)$ is not differentiable for

The set of all points where the function $f(x) = 2x|x|$ is differentiable is

The set of points where the function $f(x)=|x-1| e^{x}$ is differentiable,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module