Can someone interpret what this is asking for I have this programming problem, but I really cant figure out what it wants me to do. Heres what it is:


  The cube root of a number can be found based on the observation that, if $t$ is an approximation of the cube root of $a$, then $\tfrac13\left(\tfrac{a}{t^2} + 2t\right)$ is a better approximation. 
  
  Create a method double betterCubeRoot(double a, double t) that will find the cube root of $a$ accurate enough so that the difference between $t^3$ and $a$ is less than 0.0001. Use recursion.
  
  Then write the method double cubeRoot(double a) that makes use of the method with 1 as the initial value of $t$. Write a program that will test values both positive and negative.


Can someone please explain what this means. I dont understand how I am supposed to find the cube root of 'a' using the given equation. Thanks.

Here is what i have done:

public static double betterCubeRoot (double a, double t)
{
    double tCubed = Math.pow (t, 3);
    double dif = Math.abs (tCubed - a);

    double eq = ((a / (t * t)) + 2 * t) / 3;

    if (dif &lt; 0.001)
    {
        return eq;
    }
    else
    {            
        return betterCubeRoot (eq, t) ;
    }
}
Guess anything at all for the cube root of $a$: call that value $t$. $t′=\tfrac13(a/t^2+2t)$ is closer to $\sqrt[3]{a}$ than $t$ is, so use $t′$ as your next guess. Keep going.