Q. 14.6( 5 Votes )
Show that ƒ(x) = x3 is continuous as well as differentiable at x=3.
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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