Question

Plot f(x) = x^3 - y using MATLAB. Include zero crossings in the plot.

Answer 1

What is a zero crossing?
They are such points at which a function crosses the horizontal axis as its value passes through zero and changes sign.

Given f(x) = x³ - y .
f(x) is nothing but y . Therefore f(x) = x³ - y becomes y = x³ - y   => y = 0.5 * x³

x = [-10:0.01:10];        % The range fom where to where to plot
y = 0.5 * x.^3;             % function
zci = @(v) find(v(:).*circshift(v(:), [-1 0]) <= 0);        % creating a function which returns zero-crossing indices of argument vector v
zx = zci(y);                % approximating the zero-crossing indices and storing it in zx
figure(1)
plot(x,y,'-r')                % plotting x vs y in red colour
hold on                     % holding on to the current plot to add graphing command to exisiting plot
plot(x(zx),y(zx),'*')     % adding another graphing command to the plot i.e. the zero-crossing points and mark such points with '*'
hold off                     % hold off since all changes are done
grid                          % show grid in graph
legend('function','zero crossing')       % setting legend for the plot

HERE IS THE PLOT FOR THE ABOVE QUESTION :

500 400 300 200 100 function zero crossing 0 -100 200 300 400 -500 -10 -8 -6 42 2 4 6 8 0 0