If f(x) = begin{cases} 2a - x & text{when } - | vedclass

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

Question

(A) Given,$f(x) = \begin{cases} 2a - x & 	ext{when } -a < x < a \ 3x - 2a & 	ext{when } a \leq x \end{cases}$.First,check for continuity at $x = a$

Vedclass · Accepted Answer

$f(x)$ is not differentiable at $x = a$

Vedclass · Answer

(A) Given,$f(x) = \begin{cases} 2a - x & 	ext{when } -a First,check for continuity at $x = a$:Left-hand limit: $\lim_{x 	o a^-} f(x) = \lim_{x 	o a^-} (2a - x) = 2a - a = a$.Right-hand limit: $\lim_{x 	o a^+} f(x) = \lim_{x 	o a^+} (3x - 2a) = 3a - 2a = a$.Value of function: $f(a) = 3(a) - 2a = a$.Since $\lim_{x 	o a^-} f(x) = \lim_{x 	o a^+} f(x) = f(a)$,the function is continuous at $x = a$.Now,check for differentiability at $x = a$:Left-hand derivative: $Lf'(a) = \frac{d}{dx}(2a - x) = -1$.Right-hand derivative: $Rf'(a) = \frac{d}{dx}(3x - 2a) = 3$.Since $Lf'(a) 
eq Rf'(a)$,the function $f(x)$ is not differentiable at $x = a$.

If $f(x) = \begin{cases} 2a - x & \text{when } -a < x < a \\ 3x - 2a & \text{when } a \leq x \end{cases}$,then which of the following is true?

Similar Questions

If $f(x) = \begin{cases} \frac{1}{2}(b^2 - a^2), & 0 \leq x \leq a \\ \frac{1}{2}b^2 - \frac{x^2}{6} - \frac{a^3}{3x}, & a < x \leq b \\ \frac{1}{3}\left(\frac{b^3 - a^3}{x}\right), & x > b \end{cases}$,then which of the following is true?

If $f(x) = \min \{1, x^2, x^3\}$,then

The set of all those points,where the function $f(x) = \frac{x}{1 + |x|}$ is differentiable,is

The points at which the function $f(x) = |x - 0.5| + |x - 1| + \tan x$ does not have a derivative in the interval $(0, 2)$ are:

Let $f(x) = \begin{cases} x^2 \left| \cos \frac{\pi}{x} \right|, & x \neq 0 \\ 0, & x=0 \end{cases}$,$x \in \mathbb{R}$,then $f$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module