Numerical differentiation in MATLAB - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the forward difference approximation of the derivative.

MATLAB

h = 0.01;
x = 1;
f = @(x) x^2;
derivative = (f(x + [1]) - f(x)) / [1];

Drag options to blanks, or click blank then click option'

Ax

B0.1

Ch

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using x instead of h as the step size.

Using zero as the step size, which causes division by zero.

The forward difference formula uses a small step size h to approximate the derivative as (f(x+h) - f(x))/h.

2fill in blank

medium

Complete the code to calculate the central difference approximation of the derivative.

MATLAB

h = 0.01;
x = 2;
f = @(x) sin(x);
derivative = (f(x + [1]) - f(x - [1])) / (2 * h);

Drag options to blanks, or click blank then click option'

A2

B0.1

Cx

Dh

Attempts:

3 left

💡 Hint

Common Mistakes

Using different values for the forward and backward steps.

Using x instead of h for the step size.

The central difference formula uses (f(x+h) - f(x-h)) divided by 2h to approximate the derivative.

3fill in blank

hard

Fix the error in the code to correctly compute the numerical derivative using backward difference.

MATLAB

h = 0.001;
x = 3;
f = @(x) exp(x);
derivative = (f(x) - f(x [1] h)) / h;

Drag options to blanks, or click blank then click option'

A-

B+

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using plus instead of minus, which changes the formula.

Using multiplication or division operators incorrectly.

The backward difference formula subtracts the function value at (x - h) from f(x), so the operator must be '-'.

4fill in blank

hard

Fill both blanks to create a function that returns the central difference derivative approximation.

MATLAB

function d = central_diff(f, x, [1])
    d = (f(x + [2]) - f(x - h)) / (2 * h);
end

Drag options to blanks, or click blank then click option'

Ah

Bx

C0.01

Df

Attempts:

3 left

💡 Hint

Common Mistakes

Using x or a constant instead of the step size variable.

Using the function name f instead of the step size.

The function uses h as the step size, so both blanks should be h to correctly compute the central difference.

5fill in blank

hard

Fill all three blanks to create a function that computes the forward difference derivative with input validation.

MATLAB

function d = forward_diff([1], [2], [3])
    if h <= 0
        error('Step size must be positive');
    end
    d = (f(x + h) - f(x)) / h;
end

Drag options to blanks, or click blank then click option'

Af

Bx

Ch

Dd

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing the order of inputs.

Using variable names not related to the function inputs.

The function inputs are the function handle f, the point x, and the step size h, in that order.