Quiz 1 Chem 3730 January 16, 2006 Answer all the questions below in the space provided. You may use maple to aid in your analysis. 1) a) Plot the function, func1, over the interval 0 to 25, and sketch it below. (3 marks) func1 := ( 4 x 2 x x9 ) e 3 2 x 2 b) Find the extrema of this function over the range 0<x<25, and prove whether they are maxima or minima. (show all intermediary steps) (5 marks) c) Give the expression for the integral of func1 and determine its value over the interval from 0 to infinity. (Hint: you can set the integration limits to infinity by the word infinity) (3 marks) 2) Given the functions f(x)=2x3-2x+3, g(x)=10x, and operators O = d/dx, P = x, show that these operators have both associative and distributive properties. (4 marks)