Question #2 This question deals with the first derivative of a function f(r) on the real b) (BONUS) Produce a function derivative.comparison that has four numbers. Recall that arguments: . coefficients: a list of numbers representing the coefficients of a polynomial p() a: a number tol: a float with default value 0.01, h0 and so for small values of h, we can expect that f'(a) is close to lim-- if this limit exists. max.steps: a positive integer with default value 1000 Another way to express this is as follows: if the function f is differentiable at a then This function wil compare the exact value of p(a) computed using the function polynomial derivative from Question #1 (c) with the ap- proximate value of p'(a) obtained using the function derivative.quotient from part (a) of this question. since as n 00, (1) 0. So, for large enough values of n, this quotient should also be close to f'(a) derivative comparison(coefficients, a, tol, max steps) (a) Produce a function derivative.quotient that has three arguments will return the tuple (p'(a), q, n), where n is the smallest positive integer such that the difference between p(a) and the number q re- turned by derivative-quotient applied to p(r), a, and h = 1 is smaller than tol If the smallest such integer n is bigger than max.steps, the function should return the string 'Maximum number of steps exceeded.'. f, a, h where f is a function from float to float, a is a number, and h is a number, with default value 1e-4. derivative quotient(f, a, h) should return the number f(a h)- f(a) . You may assume that the given function f is defined at the num- For example, derivative.comparison([1, 2, 3], 10, 0.01, 10000) should return the tuple (62, 62.00996677739175, 301) since the deriva- tive of the polynomial p(x)-1 + 2x + 3r2 at a- 10 is 62, the value returned by derivative.quotient applied to p(x) with a-10 and h - 1/301 is equal to 62.00996677739175, and the difference between these two numbers is less than 0.01. On the other hand, derivative.comparison([1, 2, 3], 10, 0.0001) should return the string 'Maximum number of steps exceeded." bers a h and a For example, derivative-quotient (math.sin, 0, 0.1) should return the number 0.9983341664682815 since this is equal to (sin(0+0.1) sin(0))/(0.1). Note that in order to evaluate this particular expression you will need to import math in the console or in vou that you upload to the Avenue dropbox. r file. Do not include any import statements in the file . If h 0 your function should return the string "Division by 0 is not allowed