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-4 // 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) = 2p-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 0:2 0.4 0.6 0 8 12 1.4 1.6 1.8 f ( x ) ? --0.2 (ii) Apply numerical integration to calculate 9/4 exp (- x) 2 dx . ( You may use 3 - 5 trapezoids for this calculation; show calculation steps). 3/4 X