How can I make function and find minimum

E = problem_energy;
V = problem_volume;

[p,~,mu]=polyfit[V,E,6);

Now I have coefficient in p 1x6 How can I make polynomial equation with this and find minimum? I want to use fminsearch

Answer 1

[Star Strider]

Use the polyder function to get the first derivative (and, if you want to be efficient, the second derivative as well), then use the roots function and basic calculus to find the minimum.

Example:

p = polyfit([-1:0.01:2], cos(-1:0.01:2),6); % Polynomial Coefficients

d1p = polyder(p);                           % First Derivative
d2p = polyder(d1p);                         % Second Derivative

ips = roots(d1p);                           % Inflection Points
xtr = polyval(d2p, ips);                    % Evaluate ‘d2p’ at ‘ips’
minpts = ips((xtr > 0) & (imag(xtr)==0));   % Find Minima

x = linspace(min(ips)-5,max(ips)+5);
ep = polyval(p,x);

figure(1)
plot(x, ep, '-r')
hold on
plot(minpts, polyval(p,minpts), 'bp')
hold off
grid