Q103 / 160 · AP EAMCET 2023 (19 May Shift 1) · Mathematics
Assertion (A): If $\mathrm{f}(\mathrm{x})$ is not continuous at $\mathrm{x}=\mathrm{a}$, then it is not differentiable at $x=a$
Reason (R): If $f(x)$ is differentiable at a point, then it is continuous at that point
- Correct answerA(A) and (R) are both true, (R) is correct explanation of (A)
- B(A) and (R) are both true, (R) is not correct explanation of (A)
- C(A) is true, (R) is false
- D(A) is false, ( $R$ ) is true
Solution
If $f(x)$ is a differentiable function then $f(x)$ will be also continuous at that point necessarily. Hence reason ' $\mathrm{R}$ ' is correct. Above concept also means that if $f(x)$ is not continuous at any point $x=a$ then $f(x)$ will not be differentiable at $x=a$.
Hence, the correct answer is option: 'A'.