Finding the maximum point of a function

I would like to find the T value and Y_B value at the maximum for t=1s and t=20s

T=600:10:850;
t = 1;
k1 = 1e7.*exp(-12700./T);
k2 = 5e4.*exp(-10800./T);
k3 = 7e7.*exp(-15000./T);
t=2:2:20;
hold on;
for i=1:numel(t)
   Y_B = (k1.*t(i))./(((k2.*t(i))+1).*(1+(t(i).*(k1+k3))));
   plot(T,Y_B);
   xlabel('Temperature, T / K') 
   ylabel('Yield of Maleic Anhydride, Y_B')
   legend('\tau = 2s','\tau = 4s','\tau = 6s','\tau = 8s','\tau = 10s','\tau = 12s','\tau = 14s','\tau = 16s','\tau = 18s','\tau = 20s')
end

I know how do it this when a single function is plotted, but not when several are. How do I do this?

Answer 1

[Star Strider]

Try this:

T=600:10:850;
t = 1;
k1 = 1e7.*exp(-12700./T);
k2 = 5e4.*exp(-10800./T);
k3 = 7e7.*exp(-15000./T);
t=2:2:20;
hold on;
for i=1:numel(t)
   Y_B = (k1.*t(i))./(((k2.*t(i))+1).*(1+(t(i).*(k1+k3))));
   plot(T,Y_B);
   xlabel('Temperature, T / K') 
   ylabel('Yield of Maleic Anhydride, Y_B')
   legend('\tau = 2s','\tau = 4s','\tau = 6s','\tau = 8s','\tau = 10s','\tau = 12s','\tau = 14s','\tau = 16s','\tau = 18s','\tau = 20s')
end 

Y_B_fcn = @(t) (k1.*t)./(((k2.*t)+1).*(1+(t.*(k1+k3))));
[Y_B_max1, idx1] = max(Y_B_fcn(1));                                 % Maximum & Index At ‘t=1’
[Y_B_max20, idx20] = max(Y_B_fcn(20));                              % Maximum & Index At ‘t=20’

Y_B_max1 =
   0.48894

idx1 =
    26

Y_B_max20 =
   0.51129

idx20 =
    12

[sophp]

Hi Star Strider, thanks for this!! I do not think it is working as the idx1 and idx20 are claimed to be 26 and 12 respectively but this does not correspond with what is displayed on my graph (values should be about 700 and 850). Also, my mistake, the interval of t is between 2 and 20, I did change this when using MATLAB but it did not display the correct answer.

[Star Strider]

As always, my pleasure!

The ‘idx’ values are indices into ‘t’ (or ‘T’, since I am getting them confused).

The ‘T’ values corresponding to those indices are:

T_1 = T(idx1)
T_20 = T(idx20)

T_1 =
   850

T_20 =
   710