Let f:[0,2] ->Rbe continuous on [0,2] and differentiable on (0,2) with f(x)=0 and f(1)=f(2)=1

Show that there is a c(1) in (0,1) with f ’(c(1)) = 1

Show that there is a c(2) in (1,2) with f ‘(c(2)) = 0

Show that there is a c(3) in (0,2) with f ‘ (c(3)) = 1/3