How can I find the where the second derivative is zero?

I tried using the fzero function to solve for the root after graphing, but can't seem to get it:

>> z=[0:0.5:3];
>> T=[70 70 55 22 13 10 10];
>> plot(z,T, 'o')
>> A = spline(z,T);
>> M = diag(3:-1:1,1);
>> %first derivative
>> D=A;
>> D.coefs = D.coefs*M;
>> %second derivative
>> D1=D;
>> D1.coefs = D1.coefs*M;
>> x = linspace(z(1),z(end),1001);
>> plot(z,T,'x')
>> hold on
>> plot(x,ppval(A,x),'r')
>> plot(x,ppval(D,x),'g')
>> plot(x,ppval(D1,x),'k')
>> legend({'Original Data','Spline','First Derivative','Second Derivative'})

[Walter Roberson]

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[Jan]

Deleting a question after an answer has been posted, is very unfriendly.

[Randy Souza]

I have restored the original text of this question.

Me Yu, this question has an accepted answer, so it may be valuable to someone else in the future. If you have a good reason why it should be removed from MATLAB Answers, please flag the question, explain why it should be deleted, and an administrator or high-reputation contributor will consider deleting the question. Please do not simply edit your question away.

Answer 1

[Matt J]

Not sure what the problem is. The roots I get all seem to agree with your graph

    >> fzero(@(x) ppval(D1,x),0)

    ans =

        0.1175

    >> fzero(@(x) ppval(D1,x),1)

    ans =

        1.2162

    >> fzero(@(x) ppval(D1,x),2)

    ans =

        1.9680

    >> fzero(@(x) ppval(D1,x),2.4)

    ans =

        2.2544

[Me Yu]

thanks, how could i then find the value of the first derivative function at the z value of one of the zeros say z=1.2162?

[Matt J]

Wouldn't you just evaluate the function for the first derivative that you already have at z=1.2162?

[Me Yu]

ya thats what im trying to do but the value i get does not match the expected result of around -70, so i dont know the code

[Matt J]

I get -73.0354. Seems pretty close. If that's not what you expect, you might have to question your expectations. :D

[Me Yu]

what line of code did you use?

[Me Yu]

thats the answer i want

[Matt J]

The same code you used to plot the first derivative.

[Me Yu]

i misut be doing something wrong i continue to get -108.0295. sorry im new to matlab as im sure you can tell

[Matt J]

Show what you're doing.

[Matt J]

Hmmm. I can only assume you accidentally revised D somewhere. I get -73.0354

[Me Yu]

ok but that line of code is correct i just have to find a mistake with D?