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 answer
    A
    (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'.

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