Consider the following statements.(a) If a fu | vedclass

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

Question

(B) Statement $(a)$ is incorrect because if a function is differentiable at a point, it must be continuous at that point.Statement $(b)$ is correct be

Vedclass · Accepted Answer

$(b)$ and $(c)$

Vedclass · Answer

(B) Statement $(a)$ is incorrect because if a function is differentiable at a point, it must be continuous at that point.Statement $(b)$ is correct because differentiability implies continuity; therefore, the contrapositive (not continuous implies not differentiable) is also true.Statement $(c)$ is correct because $f(x) = |x|$ is continuous for all $x \in R$ but is not differentiable at $x = 0$.Statement $(d)$ is incorrect because $f(x) = x - [x]$ is the fractional part function, which is discontinuous at all integers, including $x = 1$. Since it is discontinuous at $x = 1$, it is not differentiable at $x = 1$.Thus, statements $(b)$ and $(c)$ are correct.

Similar Questions

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

If $f(x)=|x|+|\sin x|$ for $x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$,then its left hand derivative at $x=0$ is

If the function $g(x)=\begin{cases} K \sqrt{x+1} &, 0 \leq x \leq 3 \\ mx+2 &, 3 < x \leq 5 \end{cases}$ is differentiable, then $K+m=$

The function $f(x)=|x^{2}-2 x-3| \cdot e^{|9 x^{2}-12 x+4|}$ is not differentiable at exactly :

If $[t]$ denotes the greatest integer $\leq t$,then the number of points at which the function $f(x) = 4|2x + 3| + 9[x + \frac{1}{2}] - 12[x + 20]$ is not differentiable in the open interval $(-20, 20)$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module