Compute a FD second order approximation of the first derivative of the function f(x) = sin(x2) at x = 1.5 using x = 0.1
Compute a FD second order approximation of the first derivative of the function f(x) = sin(x2) at...
Question 2-Part B: How many inflection points for the function whose second derivative is f"(x) sin(3x)-cos(x2) for 0 < x < 3 Question 2-Part B: How many inflection points for the function whose second derivative is f"(x) sin(3x)-cos(x2) for 0
3. A five-point centered finite difference approximation to the first derivative is given by - f (x + 2h) +8f (x + h) – 8f (x – h) + f(x – 2h) 12h (a) What is the error term associated with this formula? (b) Numerically verify the order of approximation using f(x) = (1 + x2)-1 at x = 1 using the values h = 0.1, 0.01, 0.001.
My code for calculating the first derivative is the second image Compute second derivative O solutions submitted (max: 10) You are provided with a set of data for the position of an object over time. The data is sampled at evenly spaced time intervals. Your task is to find a second order accurate approximation for the acceleration at each point in time. Write a Matlab function that takes in a vector of positions x, the time interval between each sampled...
2. Consider f(x)={ x2 sin (1) xメ0 x) = (a) Show the function has a derivative for xE [0,1 (b) Show the function does not have a second derivative for x E [0,1] (c) Does this violate our understanding of holomorphic functions?
(a) A function / has first derivative f'(z) = and second derivative 3) f"(x) It is also known that the function f has r-intercept at (-3,0), and a y-intercept at (0,0) (i) Find all critical points, and use them to identify the intervals over which you will examine the behaviour of the first derivative ii) Use the f'(), and the First Derivative Test to classify each critical point. (ii) Use the second derivative to examine the concavity around critical points...
Write a C program that numerically calculates the second derivative of the function f(t) = sin(H) + 0.3A where the input&ranges [0:0.1:5). Find the second derivative at each point not including the first and last points. Also calculate the analytical solution at each point. Print to the screen the numerical and analytical results for comparison
Derive the following numerical approximation to the second derivative of f(x) using Taylor's series. Show all of your steps and derive also the order of accuracy of this approximation in terms of h. - f(x + 2h) + 16f(x + h) – 30f(x) + 16 f(x – h) – f(x – 2h) 12h2 1 (C)
D1.1. Evaluate f'(a) by using the definition of derivative of a function f(x) = 4x2 + 3x – 5 at a = -2. [4 Marks] D1.2. (a) Find the derivative of y = 4 sin( V1 + Vx). (b) If y = sin(cos(tan(x2 + 3x – 2))), then find the first derivative. [3 Marks] D1.3. Using logarithmic differentiation, find the derivative of y = (sec x)+”.
solve with matlab Given the function: f(x) x2 + 4x + et and the point f(1) = 7.7183 use Taylor series to compute the second order approximation to find the value off (1.5). Input your answer up to 4 decimal places.
Apply the second derivative test to find the relative extrema of the function f(x)=ln(x2+x+1)