Python coding question

a The Newton-Raphson Method Be sure to watch the video introducing the Newton-Raphson method before proceeding We begin our exploration of numerical methods with a cool algorithm for finding the roots (zeros) of a function: the Newton-Raphson method, sometimes simply called Newton's method. Between 1665 and 1666, Isaac Newton (1642 - 1727) spent his days under lockdown in his countryside home at Woolsthorpe, England while the Great Plague was ravaging London. During these so-called "plague years" Newton was free to think, observe, and create. His many discoveries from this productive period of his life include the development of calculus, the laws of classical mechanics, the theory of gravitation, and the workings of optics. Among these massive achievements was a little algorithmic gem that we will now discuss. The algorithm The algorithm in question - which later became known simply as "Newton's Method" or the "Newton-Raphson Method" after Joseph Raphson (c. 1648 - c. 1715) who elaborated on the algorithm - could be used to find the roots of an arbitrary function. Finding a root of a function f() just means finding a value of such that t) = 0. Newton's method involves computing a series of increasing accurate estimates of the root as follows: 1. Choose an initial value for the root, 7, and call it to 2. Compute an improved estimate x142 11 - where f[?[?][?](x) is the derivative of f(x). 3. Go back to step 2 The above generates an intinite sequence of t; In practice we stop as soon as we have a sufficiently good" estimate of the actual root, as will be explained in the information panels and questions that follow. The support functions For the next few questions, we'll be working on finding the roots for the following quadratic equation: f(x) = ?-1.5 which has the derivative: S') - 27 Before we get started on the root-finding, however, you are to write two functions that will come in handy later: *X), which takes a number or numpy array x and returns fly) as defined above. prine(x), which takes a number or numpy array x and returns f") as defined above. Paste these two functions into the answer box below. Note: Each function can easily be written using just a return statement. If you're doing more than this, you're probably overthinking it. For example: Test Result x = 2 printf(x)) print(f_prine(x)) 2.5 4 Answer: (penalty regime: 0, 10, 20, ... %) Precheck Check