I am trying to solve to the equation
f(x) = cos(x) - sqrt(x)
using Newton-Raphson Method in python
f'(x) = -sin(x) - (1/2*sqrt(x))
For my starting guess, I'm trying values form 0 to 4. It works fine from the range 0.00001 to 2.45
The graph looks like this
But my code fails (gives nan) when I enter values beyond 2.45. It also fails at 0. I'm not able to understand the mathematical logic behind this. Any help would be really helpful.