Answer :
[tex]f(x)=|x-4|\\
f'(x)=\text{sgn} (x-4)\\
\text{sgn} (x-4)=0\\
x-4=0\\
x=4\\\\
[/tex]
For [tex]x<4[/tex] [tex]f'(x)<0[/tex].
For [tex]x>4[/tex] [tex]f'(x)>0[/tex].
[tex]\Downarrow\\ [/tex]
At [tex]x=4[/tex] there's turning point, which is equal [tex]|4-4|=|0|=0[/tex].
For [tex]x<4[/tex] [tex]f'(x)<0[/tex].
For [tex]x>4[/tex] [tex]f'(x)>0[/tex].
[tex]\Downarrow\\ [/tex]
At [tex]x=4[/tex] there's turning point, which is equal [tex]|4-4|=|0|=0[/tex].
