open Impact

let redLine(a, b ,m, xlen) = 
    let mutable x = a-xlen
    let mutable xend = a+xlen
    let mutable y = b-xlen*m
    while (x < xend) do
        dot(x,y) red
        x <- x + 0.5
        y <- y + m*0.5
    dot(a,b) black


clear()


let f(x) = 2.0**x
let fprime(x,h) = (f(x+h) - f(x)) / h
//x <- 0.0               //uncomment these 4 lines to graph f(x) in pink
//while x < 200.0 do
//    dot(x,f(x)) pink
//    x <- x + 1.0

h <- 0.001
x <- 0.0
while (x < 200.0) do
    //dot(x,fprime(x,h)*10.0) red      //uncomment this line to graph f'(x) in red
    dot(x,10.0*fprime(x,h)/f(x)) green  //ratio f(x)/f'(x), scaled up by factor of 10
    m <- fprime(x,h)
    //redLine(x,f(x),m,h*2.0)    //uncomment these 2 lines to plot the tangent lines
    //dot(x,f(x)) black
    x <- x + 1.0