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 ?

Step-by-step solution

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