Q1 of 48 Page 364

Show that ƒ(x) = x3 is continuous as well as differentiable at x=3.

Given:


f(x) = x3


If a function is differentiable at a point, it is necessarily continuous at that point.


Left hand derivative (LHD) at x = 3






Right hand derivative (RHD) at x = 3






LHD = RHD


Therefore, f(x) is differentiable at x = 3.



Also, f(3) =27


Therefore, f(x) is also continuous at x = 3.


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