Eigen-Experiments
Project #3  explores working with  functions, derivatives, and ODEs.

1. This plots several functions. Replace these by three different functions which  

a. are convex over [-2,-1], 
b. are symmetric over [0,2],
c. have a discontinuity in [-3,3].

f1[x_]:=x^2;
f2[x_]:=x;
f3[x_]:= Sin[x];

plot1 = Plot[f1[x],{x,0,1}];
plot2 = Plot[f2[x],{x,-1,1}];
plot3 = Plot[f3[x],{x,0,10}];
Show[GraphicsArray[{plot1,plot2,plot3}]]

(* your work here *)

2. This plots two functions and their derivatives. Find  and plot two funtions whose
derivatives
a. have three zeroes over [0,1]
b. have a discontinuity at at x=2.
Expalin which is funtion and which is deivative.

f1[x_]:=Sin[x];
f2[x_]:=Sin[8x];

plot1 = Plot[{f1[x],f1'[x]},{x,0,1}];
plot2 = Plot[{f2[x],f2'[x]},{x,-1,1}];
Show[GraphicsArray[{plot1,plot2}]]

(* your work here *)

3. This solves the compound interest ODE and plots the solution.
Experiment with the ODE so that, after a while of increase,    the solution will decrease.

ode={y'[x]==0.07y[x],y[0]==100};
sol=NDSolve[ode,y,{x,0,30}];
Plot[Evaluate[y[x]/.sol],{x,0,10}]

(* your work here *)