How would I plot this and then achieve minimum and maximum.

This is the equation

My script looks like this and fails

x=0:0.1:15

y=(x)^3/3-11(x)^2/2+24x

plot(x,y)

Not yet got my head around MatlB

[Dyuman Joshi]

Look into

Array vs Matrix Operations

max, min - for global extremum

islocalmax, islocalmin - for local extremum

Answer 1

[Les Beckham]

x = 0:0.1:15;
% y=(x)^3/3-11(x)^2/2+24x << you were missing multiplication operators *
% and the powers need to be .^ (element-wise operator) instead of ^ (matrix
% operator)
y = x.^3 / 3 - 11*x.^2 / 2 + 24*x;
plot(x, y)
grid on
xlabel x
ylabel y

fprintf('min(y) = %f; max(y) = %f\n', min(y), max(y))

min(y) = 0.000000; max(y) = 247.500000

Also, if you are just getting started with Matlab, I would highly recommend that you take a couple of hours to go through the free online tutorial: Matlab Onramp

[Tom]

Thanks, that OnRamp is really well setup!

[Les Beckham]

That's good to hear. I hope it was helpful.

Answer 2

[Sam Chak]

Hi @Tom

The cubic function does not have global extrema, but it does have a local maximum point and a local minimum point. Are you looking to plot something similar to this?

%% Find local max and local min over a certain range
y      = @(x) x.^3/3 - 11*x.^2/2 + 24*x;
xlocal = linspace(1, 10, 90001);
ymax   = max(y(xlocal))

ymax = 31.5000

idx1   = find(y(xlocal) == ymax);
xmax   = xlocal(idx1)

xmax = 3

ymin   = min(y(xlocal))

ymin = 10.6667

idx2   = find(y(xlocal) == ymin);
xmin   = xlocal(idx2)

xmin = 8

%% Plot function over a predefined range
x      = 0:0.1:15;
plot(x, y(x)), grid on, hold on
plot(xmax, ymax, 'o', 'markersize', 12, 'linewidth', 2)
plot(xmin, ymin, 'o', 'markersize', 12, 'linewidth', 2)
xlabel('x'), ylabel('y')
xt     = [xmax-1  xmin-1];
yt     = [ymax+15 ymin+15];
str    = {'local max','local min'};
text(xt, yt, str)

[Dyuman Joshi]

I'm a curious as to why you chose to use max() and min() instead of islocalmax() and islocalmin().

[Sam Chak]

Sometimes, I'm accustomed to using functions with the same name in other software. It's good that you introduced islocalmax() and islocalmin().