Trying to plot the output of a function where h is a range over 10^-1 to 10^-18

Hello I am trying to answer this question :

Using a suitable graph, show the output of your function with x fixed at 0.25, and with values of h ranging from 10-1 to 10-18.

However it seems that I am not setting the h range the right way nor am i plotting it the right way.

function AD = absolutediff(x)

for h = 10^-1:10^-18

f = @(x) cos(x);

f1 = @(x) -sin(x);

AD = f1(x) - ((f(x+h)-f(x))./h);

plot(x,AD)

end

Answer 1

[Dyuman Joshi]

We can take advantage of the vectorization here -

AD = absolutediff(2.5)

AD = 1×35

-0.5985 -0.5985 -0.5985 -0.5985 -0.5985 0.4548 -0.0434 -0.0016 0.0122 -0.0016 -0.0001 0.0001 0.0000 0.0000 0.0000 -0.0000 0.0000 0.0000 0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0001

function AD = absolutediff(x0)
    %Function definitions
    f = @(x) cos(x);
    f1 = @(x) -sin(x);
    fun = @(x, h) f1(x) - ((f(x+h)-f(x))./h);
    
    %h values for example
    h = 10.^(-18:0.5:-1);
    
    %Calculate the value of the function for a given x and set of h-values.
    AD = fun(x0, h);
    
    %plot h vs AD as a red line with asterisks as marker
    plot(h, AD, 'r-*')
    %Adjust the x-ticks
    xticks(10.^(-18:-1))
    %Change the scale of x-axis to log for a better appearance of the graph
    set(gca, 'XScale', 'log')
end

[Dyuman Joshi]

Any updates, @Davin?