a) plot the graph of 2𝑥𝑥 �𝑢𝑢(𝑥𝑥) − 𝑢𝑢(𝑥𝑥 − 5)� + 10 (𝑢𝑢(𝑥𝑥 − 5) − 𝑢𝑢(𝑥𝑥 − 10)) for 0 ≤ x ≤ 12. describe the graph produced. in matlab

To plot the graph of the given equation in MATLAB, you can follow these steps:

1. Define the function: First, define the function 2*x^2 - heaviside(x) + 10 * (heaviside(x-5) - heaviside(x-10)) using the heaviside function in MATLAB.

2. Define the range of x: Define the range of x values you want to plot, in this case, 0 ≤ x ≤ 12.

3. Plot the graph: Use the plot function in MATLAB to plot the graph.

Here is the MATLAB code to plot the graph:

main.m
% Define the function
f = @(x) 2*x.^2 - heaviside(x) + 10*(heaviside(x-5) - heaviside(x-10));

% Define the range of x
x = 0:0.01:12;

% Plot the graph
plot(x, f(x));
grid on;

% Add labels and title
xlabel('x');
ylabel('y');
title('Graph of 2x^2 - u(x) + 10(u(x-5) - u(x-10))');

% Add legend if needed
% legend('y');

% Adjust the axis if needed
% xlim([0, 12]);
% ylim([-10, 160]);
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When you run this code, it will plot the graph of the given equation in the specified range of x values. The graph will show the relationship between x and y, and you can analyze the shape, slopes, and intercepts of the graph to describe the behavior of the equation.

Note: Uncomment the lines with % if you want to customize the graph further, such as adding a legend or adjusting the axis limits.