How can I use the Second Derivative test to find Maxima and Minima in MATLAB -

i'm looking create function takes equation , marks maxima and/or minima, , asymptotes on graph.

from calc 1, remember using second derivative test.

i started solving roots of first derivative - not sure how can plot point in vector intersect original equation.

syms x;         %//  f = sin(x)      %// define equation function df=diff(f)      %// first derivatives ddf=diff(df)    %// second derivatives 

i found roots x-values of these points dfroots = solve(df)

and created vector of them called dfroots_realdouble

dfroots_double = double(dfroots); dfroots_realdouble = real(dfroots_double); 

dfroots_realdouble represent x-values need, dont know how plot them points , separate minima maxima, etc

i'd able put in function, sin(6*(x^5) + 7*(x^3)+8*(x^2)) on [-1,1] , highlight maxima 1 marker, , minima another.

if sort roots, have alternating vector of maximums , minimums. use second derivative determine if vector of roots starts maximum or minimum , split vector.

roots = sort([-3 4 2 -5]); is_max = (subs(ddf, x, roots(1)) < 0) if is_max     max_points = roots(1:2:end)     min_points = roots(2:2:end) else     max_points = roots(2:2:end)     min_points = roots(1:2:end)    end % plot 2 different symbols plot(max_points, subs(f, x, max_points), 'or',...      min_points, subs(f, x, min_points), '*k')