MATLAB: Find and display intersections using fzero

functionsgraphintersectionsplot

I have two functions: f(x) = x.^2-1, f(g) = exp(x/5) in a linspace(-2,2). I need to indicate on the graph where f = g using the fzero function. Also I would like to keep it in a single m file.
Thanks

Best Answer

If f(x) = g(x) then f(x) - g(x) = 0. So we need to define h(x) = f(x) - g(x) and find where h(x) = 0. This is exactly what fzero is made for.
h = @(x) x.^2 - 1 - exp(x/5); % Creates a function handle for your function
Now let's plot and see if we can find a point close to where this function is zero.
x = -2:0.01:2;
plot(x,h(x));
Looks like -1.5 and 1.5 are close.
firstZero = fzero(h,-1.5);
secondZero = fzero(h,1.5);
Now visualize these on the plot:
hold on
plot(firstZero,h(firstZero),'ro');
plot(secondZero,h(secondZero),'ro'); 
hold off
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