Question

Compare and Contrast between Newton Raphson and Secant mehod.

Answer 1

The Newton method is in principle faster; its convergence is quadratic while the secant method's convergence is of order (1+sqrt(5))/2 which is about 1.6. The problem with the Newton method is that you need to be able to actually evaluate the derivative, which may be difficult for various reasons.
The Secant Method only requires one function input, f(x), but two initial guesses. It uses these to approximate the derivative then move to the x axis and repeat the process.

The Newton-Raphson Method requires two functions to be input, f(x) and f'(x), and one initial guess.

Both these methods are following the tangent line of the function to the x-axis then reiterating to bound the root.