Question

F f(x) is differentiable at x c, then a 2c and b -c . Reason A continuous function is differentiable everywhere. Medium f(x) = { x ,for x ≤ c 2 ax + b,for x > c = = = 2

A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect

Answer 1

The assertion about the values of 'a' and 'b' for differentiability at 'x=c' is correct, but the reason stating that a continuous function is differentiable everywhere is incorrect; continuity does not imply differentiability.

Step-by-step explanation:

If f(x) is differentiable at x=c, then we have the condition that a=2c and b=-c. However, the Reason given, which states 'A continuous function is differentiable everywhere,' is not correct, as continuity does not necessarily imply differentiability. In particular, a function can be continuous at a point but not differentiable there if it has a corner, vertical tangent, or discontinuity in the derivative at that point.

Answering the question: The Assertion stating the values of a and b for differentiability at x=c is correct if it's based on the conditions required to smoothly connect the two pieces of the function f(x) at the point c. The Reason, however, is incorrect as it misstates the relationship between continuity and differentiability. Therefore, the correct answer is C: Assertion is correct but Reason is incorrect.