how to draw a tangent to a data points at a given x-coordinates in matlab

Suppose I've a data like this

t=0:10:100 Ca = 50,26.1,13.6266,7.11,3.7137,1.9387,1.012, .5284, .2758, .1440, .0752

This is some experimental data of some rxn

Here I want to know the slope of tangent at some x value.

So how we draw the tangents to this data points using matlab

Answer 1

[Ameer Hamza]

Unless you have an equation describing these data points, you can only estimate the slope of tangent (derivative) using gradient() function and then interpolating the result.

For example

t = 0:10:100;
Ca = [50,26.1,13.6266,7.11,3.7137,1.9387,1.012, .5284, .2758, .1440, .0752];
dCa_dt = gradient(Ca)./gradient(t);

df = @(t_) interp1(t, dCa_dt, t_); % derivarive of Ca at any point t=t_

Result

>> df(2)
ans =
   -2.2757
>> df(45)
ans =
   -0.1968