Drawing a tangent line (concave line) for a curve

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Abdulrahman Alzailaie
回答： Devineni Aslesha 2020-2-25
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

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回答（1 个）

Devineni Aslesha
Devineni Aslesha 2020-2-25
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);

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