Define the objective function by setting its output with the opposite sign as follows:
function F=fun(x)
F=-0.2662*x.^6+48.19*x.^5-3424.2*x.^4+121708*x.^3-2*exp(6)*x.^2+2*exp(7)*x-6*exp(7);
F=-F;
end
The initial function that you presented does not have a finite global minimum, it tends to -inf due to the negative sign at the coefficient of x^6. The above function has a global minimum, so if you execute the code:
x0 = 1;
[x, fval] = fminunc (@fun,x0)
then the algorithm finds the local minimum of -fun, therefore the global maximum of fun.
