Tangents to the curves

Hello, I have plotted a few figures as shown below. Now i would like to plot the tangents to each of these curves. How can i do that?

I have searched on the forum but could not get any definitive answer.

The code for this graph is divided in 2 functions as shown below:

function [x,y_val] = plot_trial(Z)

g = 9.8; K = 0.3; % g is the gravitational accleration

y = @(V_d) (1/(2*g*K^2))*(V_d.^2/Z^2);

x = linspace(0,1,100);

y_val = y(x);

end

clc; clear; close all;

% Use the other function 'plot_trial()'
[v_d1, y_val1] = plot_trial(1);

[~,y_val2]= plot_trial(2);

[~,y_val3]= plot_trial(3);

figure
hold on
plot(v_d1, y_val1,v_d1,y_val2,v_d1,y_val3)

legend('Z=1','Z=2','Z=3')
title('Der Tank (Konstante Querschnittsfläche)')
xlabel('dV1/dt')
ylabel('Y')

Answer 1

[Star Strider]

At what point do you want to plot the tangent?

The usual approach is to use the gradient function to find the slope, then use that and the value of the function at that point to calculate the intercept. The slope and intercept then define the tangent line at that point.

Example —

x = linspace(0, 5);
y = x.^2;
h = x(2)-x(1);
dydx = gradient(y, h);

xi = 2.1;                                       % Choose An ‘x’ Value
yi = interp1(x, y, xi);                         % Corresponding ‘y’ Value
dydxi = interp1(x, dydx, xi);                   % Derivative At ‘x’
intcpt = yi - dydxi*xi;                         % Calculate Y-Intercept

figure
plot(x, y, '-b')
hold on
plot(x, dydxi*x+intcpt, '-r')
hold off
grid
legend('Data','Tangent', 'Location','NW')

EDIT —

To clarify my approach, I choose to use interp1 and gradient simply because it allows the desired ‘x’ value to be any value between the limits of the x-axis.

[Adam Danz]

Another approach is to calculate the slope and y intercept directly and then use refline().

% Choose tangent point (index value)
idx = 50;  

% Determine slope at point (p, p-1)
slope = (y_val1(idx)-y_val1(idx-1)) / (v_d1(idx)-v_d1(idx-1)); 
yint = y_val1(idx)- slope*v_d1(idx); 

% add reference line
refline(slope,yint)

[KALYAN ACHARJYA]

Hello Yash strickly follow the answer of @Star Strider & @Adam

Here I have done for one curve, Here I have used the answer from here, do the same for other two curves. You can use gradient.

% Use the other function 'plot_trial()'
[v_d1, y_val1] = plot_trial(1);
[~,y_val2]= plot_trial(2);
[~,y_val3]= plot_trial(3);
figure
hold on
plot(v_d1, y_val1,v_d1,y_val2,v_d1,y_val3)
%-------------------------
dy=diff(y_val1)./diff(v_d1)
k=60; % Which point you want Change accordingly and check
tang=(v_d1-v_d1(k))*dy(k)+y_val1(k)
hold on
plot(v_d1,tang,'r','linewidth',3)
scatter(v_d1(k),y_val1(k))
legend('Z=1','Z=2','Z=3')
title('Der Tank (Konstante Querschnittsfläche)')
xlabel('dV1/dt')
ylabel('Y')

[Yash Runwal]

Thank You Guys, I will try this and first try to understand the code. This helps a lot. If i have some doubts i will comment here.

Thank you again.

[Star Strider]

As always, our pleasure!