i NEED TO TURN (7X-3)^1/3 INTO AN ITERVATIVE FORMULA USING THE NEWTON RAPHSON FORMULA?

HOW DO I DO IT IN SIMPLE STEPS?

To convert the expression (7X - 3)^(1/3) into an iterative formula using the Newton-Raphson method, follow these steps:

Step 1: Begin by setting up the equation and finding its derivative:
- Let f(X) = (7X - 3)^(1/3).
- Calculate f'(X), the derivative of f(X). In this case, it is required to apply the chain rule.
- f'(X) = (1/3) * (7X - 3)^(-2/3) * 7

Step 2: Choose an initial guess value, denoted by X₀, close to the actual solution. This could be any value, but picking one close to the actual solution can allow for faster convergence.

Step 3: Apply the Newton-Raphson formula to calculate the next approximation, denoted by X₁:
- X₁ = X₀ - f(X₀) / f'(X₀)

Step 4: Use the value of X₁ to repeat Step 3 iteratively until the desired level of accuracy is achieved. Each subsequent approximation, Xn, is calculated as follows:
- Xn = Xn-1 - f(Xn-1) / f'(Xn-1)

By repeatedly applying the Newton-Raphson formula, the iteration will converge towards the actual solution of the equation (7X - 3)^(1/3).

Note: It is important to consider convergence criteria, such as determining the desired level of accuracy or setting a maximum number of iterations, to prevent infinite loop situations.