11. [Maximum mark: 23] The function f is dened as f (x) = e33r+1 , x e lit. (a) (i) (ii) Find f"(x). State the domain of f '1. The function g is defined as g (x) = lnx , x E IR+ . The graph of y = g (x) and the graph of y = f" (x) intersect at the point P. (b) Find the coordinates of P. The graph of y = g (x) intersects the x-axis at the point Q. (o) A region R is bounded by the graphs of y = g (x) , the tangent T and the line 9: = e. (d) (E) Show that the equation of the tangent T to the graph of y=g(x) at the point Q is y=x1. Find the area of the region R. (i) (ii) Showthat g(x)Sxl, xelR'. By replacing x with l in part (e)(i), show that x_1 S 3(x), x E R'. x J: [4} {5} [3] {5} [6}