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@DanielxAK Can you help me through this problem. It seems quite simple

\(S_0(x)=1+2x-x^3 \to 0 \leq x \leq 1\)
\(S_1(x)=2+b(x-1)+c(x-1)^2+d(x-3)^3 \to 1 \leq x \leq 2\)

Yes I figured it out
\(S_0'(1)=S_1'(1)\)
\(S_0''(1)=S_1''(1)\)
\(S_1''(2)=0\)
THHAANKKSSSS :)

Oh i forgot to mention that it is a natural spline lol

Gotcha Can i dirve you crazy with one more question?

Go for it. I'm trying to avoid my own homework as it is.

I think I am allowed to use a computer program but \i am wondering How can this be done by hand

Or is it wayyy too time consuming?

ohhhh it didnt work out uughhhhh

whtvrrrr ok once i get the 16 diff values then what?

It seems like I am suppossed to integrate but not sure y we are integrating

ok I will write out all the equations then

So there are my four equations

Have you tried plotting them? If those are correct, they should match f(x) = cos(pi*x) pretty well.

hmm let me try

ummm pretty much sooo

Its weird that one of the equations has nothing to do with the graph at all

Yeah, only looks like one or two of them are correct. You may want to double check your equations.

ohhh I found my mistake mixed up signs
Its only suppossed to match from [0,1] and it does

Thats cooollllllllllllllllllll

its annoying to work with sooooo mannnyy decimals

So now i integrate?

Yes. Now you can integrate using those cubics (so, from 0.25 use S1, 0.25 to 0.5 use S2, etc.).

I am just wondering y we are integrating lol
I am just not seeing the logic behind that?

You're welcome.

@DanielxAK hahah I have one more question
It asks me to find f'(.5)
How would I go abt it?

Do I add all the equations together and that will be my spline function?

Heyyyy :)

It sounds like it's just asking you to find the derivative of f(x) = cos(pi*x) at 0.5.

No it asks me to compare both so it cant mean that

Ohhh what i did for a previous question gottcchhhaaaaaaa

I am seriously driving u crazy here. Thanks I really appreciate your help

Ha. That's okay.