Code in Python only please.

PROBLEM 1: We saw in quiz 3 that the maxima (or minima) of a function can be determined by supplying the derivative as input to a root-solving algorithm like Newton's method. What if the derivative is not easy to determine by hand? The following problem combines finite differences with root-finding algorithms to do this ... The trajectory of the position of a particle is given by x(t)=2t2+1e50tcos2(2t) Find the time when where the velocity dx/dt is 0.25 . First use central differences to create a function that gives the derivative of x(t) and then use or on this function. Plot to get good initial guesses for your root-finding method