Question

Assertion: f(x) = `{(1 + x",", x ≤ 2), (5 - x",", x > 2):}` 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.e., Lf'(a) = Rf'(a).

Options

• Both Assertion and Reason are true and Reason is the correct explanation for Assertion.

• Both Assertion and Reason are true but Reason is not the correct explanation for Assertion.

• Assertion is true and Reason is false.

• Assertion is false and Reason is true.

Answer 1

Both Assertion and Reason are true and Reason is the correct explanation for Assertion.

Explanation:

The Left Hand Derivative is 1, and the Right Hand Derivative is −1. Since these values are not equal, the function is not differentiable at, which directly proves the Reason is the correct explanation for the Assertion.