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 x9 ) 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)