Find the second derivative of an integral function

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Yaser Khojah
Yaser Khojah 2018-10-11
编辑： Bruno Luong 2018-10-12
Can anyone please help me with this problem. I have an integral function that I would like to differentiate it twice to find if it is convex or not. I'm not really sure how to do it in MATLAB. First, I have to find the second derivative by MATLAB to compare to my analytical answer. Here is the function. integral of f with respect to t from t0 to ts. f and the rest as below:
if true
% code
syms price lamda t r t0 ts
fun = price .* exp(-lamda .* t) .* r;
x = int(fun,t,[t0 ts])
Y = diff(X)
end
I do not need to integrate f, I just need to find its second derivative and this function happens to be an integral.
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Yaser Khojah
Yaser Khojah 2018-10-12
This is my function. I think what you sent will not give me what I want.
Bruno Luong
Bruno Luong 2018-10-12
编辑：Bruno Luong 2018-10-12
Yes it does.
* dfun/dr = integral in [t0 ts] of price*exp(-lamda*t) dt;
* d^2fun/dr^2 = 0
You can pull out r out of the integral if it helps you to understand, since it does not depends on the integration variable t.

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