# 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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