How can i get local maxima,minima and inflection point displayed in the graph

hi, i am trying to write a function using fplot to plot a function and its first derivative and second derivative. i am able to plot the graph by simply running the function but how can i display the points automatically that indicate which is local maxima, minima and inflection point. i have a picture to show what i am getting at this moment. i am a begginner here for matlab

my code is here

function Output = Q2

figure;

lmaxPlot=[];
lminPlot=[];
inflPlot=[];
verAsymPlotBottom=[];

syms x;
func = (2*x^4 - 40*x^3 + 299*x^2 - 989*x + 1219)/(x^2 - 10*x + 23);

% place your work here
assume(x,'real');
firstdiff=diff(func); %we differentiate here with respect to x
disp(firstdiff);
seconddiff=diff(firstdiff);% we differentiate here with respect to x the result of firstdiff;



fplot1 = fplot(func,[2,8],'b-'); %plot the first function without derivation.
ylim([-15,30]);%set the Ylimits of the graph.
hold on %avoid function override
fplot2 = fplot(firstdiff,[2,8],'r-'); %plots the second function
ylim([-15,30]); 
hold on %avoids function override
fplot3 = fplot(seconddiff,[2,8],'y-'); %plots the third function
ylim([-15,30]);
hold on

% firstdiffsol = solve(firstdiff == 0,x, 'Maxdegree', 4);
% lmaxPlot= vpa(firstdiffsol,6);
% plot(lmaxPlot,subs(func,lmaxplot),'ro');
% hold on

fplotH = {fplot1;fplot2;fplot3};% here we are passing an array of output for fplots. in which all values passed are plots of function in same graph.

legendArray = {'f(x)',"f'(x)","f''(x)"};    

legendArray = [legendArray, {'Local Minima'}];        

legendObject = legend(legendArray);
set(legendObject, 'Location', 'north')

Output = {fplotH; lmaxPlot; lminPlot; inflPlot; verAsymPlotBottom}; 
end

Answer 1

[Sunand Agarwal]

Hello,

Please refer to the following link for an example of showing the critical and inflection points in a MATLAB graph:

https://www.mathworks.com/help/symbolic/find-asymptotes-critical-and-inflection-points.html

Hope this helps.