Marking x intercepts on graph

Sorry everyone. I'm pretty new to matlab. My question was to graph an equation V against x for -4</= x </=4

This is the code I came up with:

x=linspace(-4,4);
V=(x.^3/3)-4*x;

plot(x,V)
xlabel('Position'),ylabel('Potential Energy')

I need to mark the x-intercepts on the graph. How do I go about doing that?

Answer 1

[Adam Danz]

Method 1: solve equation for y=0

Use the Symbolic Math Toolbox to solve for y=0; see inline comments for details.

% Solve for y=0
syms x
eqn = x.^3/3-4*x == 0; 
xInt = double(solve(eqn)); % X values where y=0
yInt = zeros(size(xInt));  % Corresponding y values (all 0)

% plot function and x-intercepts
x=linspace(-4,4);
V=(x.^3/3)-4*x; 
plot(x,V,'k-')
hold on
plot(xInt,yInt, 'm*','MarkerSize', 10)
yline(0) 

Method 2: use intersections() to find x-intercepts

This uses the intersections() function from the file exchange to find the (x,y) coordinates of the x-intercepts.

x=linspace(-4,4);
V=(x.^3/3)-4*x;

[xInt,yInt] = intersections(x,V,x,zeros(size(V))); 
% ^^   ^^  There are your intercept coordinates

plot(x,V,'k-')
hold on
plot(xInt,yInt, 'm*','MarkerSize', 10)
yline(0)

Both methods produce this figure

[Daniel Matthew]

Thank you!

[Adam Danz]

@Daniel Matthew, I just added "Method 1" to my answer. It uses the Symbolic Math Toolbox to solve your equation for y=0 and therefore does not depend on a 3rd party FEX function.

[Abdennaser Hadab]

The second method pops an error:

Undefined function 'intersections' for input arguments of type 'double'.

Any idea what is wrong?

[Adam Danz]

@Abdennaser Hadab, the sentence under the "Method 2" heading tells you the answer and has a link :)

[Abdennaser Hadab]

@Adam Danz thanks, I have been a bit confused but I realized I needed to download the file and put it in the same folder where my .m file is in order to call for the function with no issues.

I did not know I had to do this.

[Adam Danz]

@Abdennaser Hadab, you figured it out! You can either add the file to the same folder containing the main m-file or you can store the file anywhere and make sure you add the path to the file using addpath in the m-file.

[Abdennaser Hadab]

@Adam Danz thank for the tip!

[Shyamini]

@Adam Danz Thank you so much!! this helped tremendously