Mathematics

Problem

The function

h

is defined by

h(x)=\begin{cases}x^{2}, & x \le 1,\\ 3x-2, & x>1.\end{cases}

(i) Compute the left-hand derivative

h'(1^-)

. (ii) Compute the right-hand derivative

h'(1^+)

. (iii) On the basis of your results, state whether

h'(1)

exists and justify your conclusion.