Show that the function f(x) = |x - 4|, x ∈ mathbbR is continuous, but not differentiable at x = 4.

$f(x)=|x-4|$ is continuous at $x=4$ but not differentiable there. Continuity: $f(x) = 4-x$ for $x<4$ and $x-4$ for $x\ge4$. $\lim_{x\to4^-}f(x) = 0$, $\lim_{x\to4^+}f(x) = 0$, and $f(4) = 0$. All three are equal, so $f$ is continuous at $x=4$. Differentiability: $Lf'(4) = \lim_{h\to0^-}\frac{f(4+h)-f(4)}{h} = \lim_{h\to0^-}\frac{-h}{h} = -1$ $Rf'(4) = \lim_{h\to0^+}\frac{f(4+h)-f(4)}{h} = \lim_{h\to0^+}\frac{h}{h} = 1$ Since $Lf'(4)\neq Rf'(4)$, $f$ is not differentiable at $x=4$. Hence $f$ is continuous but not differentiable at $x=4$.