forward approximation of derivative

I'm trying to figure out how to plot the forward approximation of the derivative of 1000^(x/17) at x=3.2 for h values of 0.01 to 5 in steps of 0.05. Here is what i have so far.

 clear; close all; clc;

 delx = 0.05;
 x = 0.01:delx:5;

 y = 1000.^(x/17);

 fig = figure();
set(fig,'color','white');
plot(x,y,'linewidth',2);
xlabel('x');
ylabel('y');
grid on;

 yforward = (y(2:end-1) - y(1:end-1))./delx;
hold on
plot(x(1:end)-delx/2,yforward,'r-','linewidth',2);

I'm getting an error that says matrix dimensions must agree. I also don't know how to plot the derivative at x = 3. Any help appreciated.

Answer 1

[Titus Edelhofer]

Hi,

first of all, your yforward should be

yforward = (y(2:end) - y(1:end-1))./delx;

which is in fact the same as

yforward = diff(y) ./ delx;

When it comes below to plotting: your last point has no forward derivative anymore, therefore yforward is shorter than x by one element. Try to plot

plot(x(1:end-1)-delx/2,yforward,'r-','linewidth',2);

Titus

[ray sanchez]

Thanks that was helpful! I'm still trying to figure out how to output the value for both at x=3.2 and the error.

[Titus Edelhofer]

Hi,

look for the entry in x closest to 3.2:

[~,idx] = min(abs(x-delx/2-3.2));

Get the derivative at this point:

der = yforward(idx);

and plot the line:

h=plot(x(1:end-1)-delx/2, y(idx) + (x(1:end-1)-delx/2-3.2) * der);

That should also help with your question, otherwise please reformulate ...

Titus