Consider the following statements. a) If a function is differentiable at a point ' p ' then it is not continuous at ' p ' b) If a function is not continuous at x = a , then it is not differentiable at x = a c) If f x = x then f ( x ) is not differentiable but continuous on ℝ d) If f x = x - x , then f ' ( 1 ) = 1 Which of the above statements are (is) correct?

Question

Consider the following statements. a) If a function is differentiable at a point ' p ' then it is not continuous at ' p ' b) If a function is not continuous at x = a , then it is not differentiable at x = a c) If f x = x then f ( x ) is not differentiable but continuous on ℝ d) If f x = x - x , then f ' ( 1 ) = 1 Which of the above statements are (is) correct?, Only (b), (b) and (c), Only (c), (c) and (d)

MARKS App · Accepted Answer

We know, if a function is continuous at a point x = a then it is not necessarily differentiable at the point x = a and if a function differentiable at a point x = a then it must be continuous at x = a . f ( x ) = x is continuous at every point but it is not differentiable at x = 0 . f ( x ) = x - [ x ] is not differentiable at x = 1 because the greatest integer function is discontinous at the integral points and hence not differentiable at the integral points. Hence, only (b) and (c) are true.

Search any question & find its solution

Looking for more such questions to practice?