let xMax = 3.5;

let yMin = -4;

let yMax = 2;

let xScale = 1;

let yScale = 1;

let a = 1;

let b = 3;

​

// f(x) = x^5 - 2x^4 - 1

function f(x) {

  return x*x*x*x*x - 2*x*x*x*x - 1;

}

​

// Loop to graph points of f(x)

function graphF() {

  stroke('green');

  for(let x = xMin; x <= xMax; x += 0.0001) {

    let y = f(x);

    point(x, y);

  }

}

​

function setup() {

  createCanvas(800, 800);

  xScale = width / (xMax - xMin);

  yScale = height / (yMax - yMin);

  // Slow down animation

  frameRate(1/2);

}

​

function draw() {

  background(220);

  strokeWeight(3);

  // Set display location and size based on x and y max and min & cavas size.

  translate(width * (0 - xMin)/(xMax - xMin), height * yMax/(yMax - yMin));

  scale(xScale, -yScale);

  // Draw axes

  stroke(0);

  strokeWeight(1/yScale);

  line(-width/2, 0, width/2, 0);  //x-axis

  strokeWeight(1/xScale);

  line(0, height/2, 0, -height/2);  //y-axis

  // Draw tick marks on x-axis

  strokeWeight(4/yScale);

  stroke(0);

  let min = Math.floor(xMin);

  let max = Math.floor(xMax);

  for(let x = min; x <= max; x++) {

    point(x, 0);

  }

  // Graph function

  strokeWeight(2/(xScale + yScale));

  graphF();

  /*** Plot points and functions below ***/

  strokeWeight(6/yScale);

  stroke('red');

  point(a, 0);

  stroke('blue');

  point(b, 0);

  BisectionMethod();

}

​

let i = 1; // counts the iterations of the method

let c = 0; // c will be the midpoint value of a and b in the bisection method

function BisectionMethod() {

  let n = 100; // to avoid an infinite loop

  let fc = f(c);

  let tol = 0.01;  //tolerance of the method

​

​

  if (i <= n) {

    console.log("\nBisection Method:");

    console.log("a = " + a + "\t\tb = " + b);

    c = (a + b) / 2; // middle of interval (a, b)

    fc = f(c);

    console.log("f(" + c + ") = " + f(c));

    if (fc == 0 || (b - a) / 2 < tol) {

      console.log("The root approximation is: " + c);

      console.log("The number of steps is: " + i);

      i = n + 1;

    }

    i++;

    if (f(a) < f(b)) { // f increaseing from a to b

      if (fc < 0) {

        a = c;

      }

      else {

        b = c;

      }

    }

    else if (f(a) > f(b)) { // f decreasing from a to b

      if (fc > 0) {

        a = c;

      }

      else {

        b = c;

      }

    }

  }

​

} // end of Bisection Method

​