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

Question

Philoid · Accepted Answer

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.

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