The function fis defined by f (x) = (x + 1), here pe R. 8. Show that f'(x) = (p(x + 1 ) + 1 ). E Let f (")(x) denote the result of differentiating f (x) with respect to x, n times. Use mathematical induction to prove that f (n ) ( x ) = 01- 1 ex ( p ( * + 1 ) + n ) , ne It . When p = V3 , there is a minimum point and a point of inflexion on the graph of f. Find the exact value of the x-coordinate of the minimum point; E the point of inflexion. Let p = - . Let R be the region enclosed by the curve, the x-axis and the lines x = -2 and x = 2. Find the area of R. (Total 13 marks