Question

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

Answer 1

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

LHD = RHD T

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

\(\lim\limits_{x \to 3}\) f(x) = \(\lim\limits_{x \to 3}\) x³ = 3³ = 27

Also, f(3) =27 

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