Question 6. * exp(-X ) denote the exponential function e -x) ; e=2.718 .... is the base for natural logarithm. For example, at x = 2, exp(-2") = -1:2 el - 2") = e- // In particular, the function g(x) =exp(-x2) is shown as in the right figure. 0.8 0.6 (i) Find the maximum value for function f(x) = x2P-1exp(-x ) , where p20 is a parameter. 0.4 0,2 At what value of x does function f(x) achieves its maximum? If p = 3, at what point is the maximum of -0.2 0:2 0.4 0.6 0.8 12 1.4 16 1 8 2.2 f (x ) ? -0.2 (ii) Apply numerical integration to calculate 2 9/4 exp(-x) dx .( You may use 3 - 5 trapezoids for this calculation; show calculation steps). 3/4 X