Question

For \[f(x)=|x|\], what is the left-hand derivative at \[x=0\]?

Options

• \[-1\]

• \[1\]

• \[0\]

• The left-hand derivative does not exist.

Answer 1

For negative \[h\], \[|h|=-h\], so \[\frac{|h|-0}{h}=-1\]. Hence, \[\lim_{h\to0^-}\frac{|h|-0}{h}=-1\].