If f(x) is differentiable at x=a, then consider the following statements : I. f(x) is continuous at x=a II. _ x a f(x)=f(a) Which of the statements given above is/are correct ?

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Correct answer: C. Both I and II

If a function f(x) is differentiable at a point x=a, then it is necessarily continuous at that point. This makes Statement I correct. By the definition of continuity at a point x=a, the limit of the function as x approaches a must be equal to the value of the function at a. Thus, _ x a f(x)=f(a). This makes Statement II correct. Therefore, both statements I and II are correct. Answer: Both I and II

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