how to find when the function reaches its maximum value and calculate a value at a certain point

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nguyễn gia bảo 2019-5-30

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https://ww2.mathworks.cn/matlabcentral/answers/464697-how-to-find-when-the-function-reaches-its-maximum-value-and-calculate-a-value-at-a-certain-point

编辑： dpb 2019-5-30

i have this function:

function ydot= fossil_fuels(t,y)
    p=y(1); sigmas=y(2); sigmad=y(3); alphas=y(4); alphad=y(5);
    r=[0.0 0.0 1.0 4.0 5.0 8.0 10.0 10.5 10.0 8.0 3.5 2.0 0.0 0.0];
    yr=[1000 1850 1950 1980 2000 2050 2080 2100 2120 2150 2225 2300 2500 5000];
    f=pchip(yr,r);
    d = 8.65;
    mu1 = 4.95 * 10^2;
    mu2 = 4.95 * 10^(-2);
    vs = 0.12;
    vd = 1.23;
    w = 10^(-3);
    k1 = 2.19 * 10^(-4);
    k2 = 6.12 * 10^(-5);
    k3 = 0.997148;
    k4 = 6.79 * 10^(-2);
    hs = (sigmas-(sigmas^2 - k3*alphas*(2*y(2) - alphas))^0.5)/k3;
    cs = (alphas - hs)/2;
    ps = k4*(hs^2 / cs);
    dpdt = (ps - p)/d + ppval(f,t) /mu1;
    dsigmas_dt = (1/vs)*((sigmad - sigmas)*w - k1 - ((ps - p)/d)*mu2);
    dsigmad_dt = (1/vd)*(k1 - (sigmad - sigmas)*w);
    dalphas_dt = (1/vs)*((alphad - alphas)*w - k2);
    dalphad_dt = (1/vd)*(k2 - (alphad - alphas)*w); 
    ydot = [dpdt; dsigmas_dt; dsigmad_dt; dalphas_dt; dalphad_dt];
end 

Now i was asked to find when does p reach its maximum, how ever i can only find the maximum value but don't really knowing how to find when, can somebody help me.

and also if possiple does anybody know how to calculate p only from the function at a certain t

thanks