Shortest distance from a point to this curve

Question

I need to find the distance of multiple points to a curve of the form: f(x) = a^(k^(bx))

My first option was using its derivative, using a line of the f

Answer 1

To find distance from point to curve it's not a simple task, for that you need to find the global of function where f(x) is the function which determine your curve.

For that goal you could use:
Simplex method
Nelder_Mead_method
gradient_descent

This methods implemented in many libraries like Solver Foundation, NMath etc.