Project 1

Last revision:  January 15 1998

Author: YourNameGoesHere

Functions Both Social and Secure

Jane Doe's social security number is 432-10-9876.  With it, Jane associates an eighth degree polynomial, \(TraditionalForm
      \`4  x\^8 - 3  x\^7 + 2  x\^6 - 1  x\^5 + 0  x\^4 - 9  x\^3 + 8  x\^2 - 
        7  x + 6\):

janePoly[x_] := 
 4 x^8 - 3 x^7 + 2 x^6 - 1 x^5 + 0 x^4 - 9 x^3 + 
 8 x^2 - 7 x + 6

by using the digits of her SSN as coefficients and alternating their signs.  (+,-,+,-,...)

(a)	Enter in the SSN polynomial for yourself and your partner.  If you don't have a partner, or if you must work on this project independently, then make up a suitable 9-digit number.  Note:  if the first digit of your SSN is zero, substitute a 1 for the purposes of this assignment.

(b)	Plot both polynomials on the same axes.  Remember that Mathematica distinguishes a variable from a function by the use of square brackets; hence, you do not want to plot "janePoly", say, but "janePoly[x]".

(c)	If you plot your SSN's on the interval [-20,20], they should both get very large and positive.  Plotting on smaller intervals should show you more detail.  Whose polynomial gives the smallest (or most negative) value?

(d)	Where do your SSN's intersect the x-axis?  (Hint:  The plot might give you an idea, but use "NSolve[]" or "FindRoot[]" to approach the problem.)

(e)	Where do your SSN's intersect each other?   (If the answer is nowhere then add the constant 100 to the polynomial that won in part (c). Again, consider "NSolve[]" and "FindRoot[]".)

(f)	Where do your SSN's intersect the graph of y = (e^x)?  (Hint:  Mathematica knows the constant e as "E".)