Question

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

Options

• The right-hand derivative does not exist.

• \[-1\]

• \[1\]

• \[0\]

Answer 1

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