Drawing a tangent line (concave line) for a curve

I would like to draw the line in red, i.e. the steepest line starting from (1,0) and touching the CSTR line, using MATLAB (picture attached).

Here is my code:

global k to CA0

CA0= 1;
k= [0.01 5 10 100];
tspan= [0:0.001:8];
C_init= [CA0 0]';

ts= 0.001;          %step time
tf=8;               %final time
tx= 0;              %counter
sze= 1+ (tf/ts);    %size (for loop)

for x= 1 : sze

    to= tx;
    CSTR= (fsolve(@ZMA, C_init))';
    tx = tx + ts;
    sTore(x,:)= CSTR;

end

plot(sTore(:,1), sTore(:,2));   %plot CA vs. CB
title('[A] vs. [B]')

%For CSTR
function CAB = ZMA(C)

global k to CA0

fA= to*(k(1) * C(1) - k(2) * C(2) + k(4) * C(1)^2) - CA0 + C(1);
fB= to*(k(1) * C(1) - k(2) * C(2) - k(3) * C(2)) - C(2);

CAB = [fA;fB];

end

Answer 1

[Devineni Aslesha]

Considering the curve equation as f(x), find the derivative of the curve w.r.to the variable the curve depends on i.e. ‘x’. Evaluate the derivative at the given point on the curve i.e. ‘x0’. The tangent is obtained from the line equation as shown below.

y = f(x0) + f’(x0)*(x – x0);