code in pytorch

Use torch and matplotlib for the following 1. A second order forward approximation to the derivative is f(x + 2h) - 4f(x+h) + 3f (r) $' (r) = +O(12) 2h (a) Given a function sampled at f = [f(x0), f(x1),..., f(In-1)] write a function that approxi- mates the derivatives at points (-0,21,..., In-3) and uses this approximation. (b) Design and execute testing that show that the code works as the theory predicts. 2. In this question you will derive an approximation for the second derivative pf 5. L) (a) Write the Taylor's expansion for f(x + h) around f using the first 4 terms f(a+h) = f(x) + ... (b) Write the Taylor's expansion for f(x-h) around / using the first 4 terms f(x+h) = f(x) - ... (c) Add the equations (d) Isolate S"() (e) What is the order of the approximation? Use torch and matplotlib for the following 1. A second order forward approximation to the derivative is f(x + 2h) - 4f(x+h) + 3f (r) $' (r) = +O(12) 2h (a) Given a function sampled at f = [f(x0), f(x1),..., f(In-1)] write a function that approxi- mates the derivatives at points (-0,21,..., In-3) and uses this approximation. (b) Design and execute testing that show that the code works as the theory predicts. 2. In this question you will derive an approximation for the second derivative pf 5. L) (a) Write the Taylor's expansion for f(x + h) around f using the first 4 terms f(a+h) = f(x) + ... (b) Write the Taylor's expansion for f(x-h) around / using the first 4 terms f(x+h) = f(x) - ... (c) Add the equations (d) Isolate S"() (e) What is the order of the approximation