Study the monotonicity of the following function without using differentiation and continuity? $$f(x) = 3|4-x|$$ I have changed the function to the following: $$f(x) = \left\{ \begin{array}{ll} 12 - 3x & { x\leq 4}, \\ 3x - 12 & {x> 4} \end{array} \right. $$
Then I want to divide my solution to 2 cases:
(a) $\forall$ $x_1,x_2$ $\in ]-\infty, 4 [$
(b) $\forall$ $x_1,x_2$ $\in ]4, \infty [$
And then in each of the two cases I will try to reach to the shape of the function in the above piecewise definition, but I have a problem in the first case because $x$ will take positive and negative values, so what shall I do?
Any help will be appreciated.