Register

differentiable

707 views
3 votes
3 votes

The function f: \mathbb{R} \rightarrow \mathbb{R}  is defined as follows.

f(x) = \left\{\begin{matrix} 3x^2\ if \ x \in Q \\ -5x^2\ if \ x \notin Q \end{matrix}\right.

Which of the following is true?
(A) f is discontinuous at all
(B) f is continuous only at x = 0 and differentiable only at x = 0.
(C) f is continuous only at x=0 and non differentiable at all x \in \mathbb{R}
(D) f is continuous at all x \in \mathbb{Q} and non differentiable at all x \in \mathbb{R}

User Avatar

Please log in or register to answer this question.

Voting & Accepting an answer helps improve the community
← PreviousNext →
← Previous in categoryNext in category →

Related questions

0 votes
0 votes
0 answers
1
bts asked Jun 25, 2018
392 views
Differentiable
Why is a function not differentiable at x=k when f'(x) limits to infinity? Limit can be infinite too?
Why is a function not differentiable at x=k when f'(x) limits to infinity? Limit can be infinite too?
User Avatar
0 votes
0 votes
2 answers
2
Arjun asked Sep 23, 2019
722 views
ISI2014-DCG-29
If $f(x) = \sin \bigg( \dfrac{1}{x^2+1} \bigg),$ then $f(x)$ is continuous at $x=0$, but not differentiable at $x=0$ $f(x)$ is differentiable at $x=0$, and $f’(0) \neq 0$ $f(x)$ is differentiable at $x=0$, and $f’(0) = 0$ None of the above
If $f(x) = \sin \bigg( \dfrac{1}{x^2+1} \bigg),$ then$f(x)$ is continuous at $x=0$, but not differentiable at $x=0$$f(x)$ is differentiable at $x=0$, and $f’(0) \neq 0$...
User Avatar
0 votes
0 votes
2 answers
4
gatecse asked Sep 18, 2019
440 views
ISI2015-DCG-57
Let $y=\lfloor x \rfloor$, where $\lfloor x \rfloor$ is greatest integer less than or equal to $x$. Then $y$ is continuous and many-one $y$ is not differentiable and many-one $y$ is not differentiable $y$ is differentiable and many-one
Let $y=\lfloor x \rfloor$, where $\lfloor x \rfloor$ is greatest integer less than or equal to $x$. Then$y$ is continuous and many-one$y$ is not differentiable and many-o...
User Avatar
Link Copied!