‹ Back to the paper
Study the Assertion and Reason and choose the correct option.
f(x) = {1 + x, x ≤ 2; 5 - x, x > 2} at x = 2 is not differentiable.
Assertion: $f(x) = \begin{cases} 1 + x, & x \le 2 \\ 5 - x, & x > 2 \end{cases}$ at $x = 2$ is not differentiable.
Reason: A function is said to be differentiable at $x = a$ if Left hand derivative is equal to Right hand derivative i.e., $Lf'(a) = Rf'(a)$.
- aBoth Assertion and Reason are true and Reason is the correct explanation for Assertion.
- bBoth Assertion and Reason are true but Reason is not the correct explanation for Assertion.
- cAssertion is true and Reason is false.
- dAssertion is false and Reason is true.
Answer
Answer
Correct option: a
The left-hand derivative at $x = 2$ is $Lf'(2) = 1$ and the right-hand derivative is $Rf'(2) = -1$. Since $Lf'(2) \ne Rf'(2)$, the function is not differentiable at $x = 2$, so Assertion is true. The Reason correctly states the condition for differentiability and explains why the Assertion holds.
Answer: (a) Both Assertion and Reason are true and Reason is the correct explanation for Assertion.