The function h(x)=ex−2x is defined and continuous on the interval [0,2].
(i) Compute the average value of h on [0,2].
(ii) Show that the equation h(c)=hˉ has exactly one solution in (0,2). Explain why no other solution can occur.
(iii) Using a suitable numerical method, refine the value of c correct to three decimal places. Show all iterative steps used.