Assertion (A): If f(x) is not continuous at x | vedclass

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(A) fundamental theorem in calculus states that if a function $f(x)$ is differentiable at a point $x=a$,then it must be continuous at that point $x=a$

Vedclass · Accepted Answer

$(A)$ and $(R)$ are both true,$(R)$ is the correct explanation of $(A)$

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(A) fundamental theorem in calculus states that if a function $f(x)$ is differentiable at a point $x=a$,then it must be continuous at that point $x=a$.The contrapositive of this statement is: if $f(x)$ is not continuous at $x=a$,then $f(x)$ is not differentiable at $x=a$.Since the Reason $(R)$ provides the direct theorem that justifies the Assertion $(A)$,both are true and $(R)$ is the correct explanation of $(A)$.

Assertion $(A)$: If $f(x)$ is not continuous at $x=a$,then it is not differentiable at $x=a$.
Reason $(R)$: If $f(x)$ is differentiable at a point,then it is continuous at that point.

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Assertion $(A)$: If $f(x)$ is not continuous at $x=a$,then it is not differentiable at $x=a$.Reason $(R)$: If $f(x)$ is differentiable at a point,then it is continuous at that point.