Quadratic least squares equation

[tza5021]

f(x) = –3√x, 1 ≤ x ≤ 4
(a) Find the quadratic least squares approximating function g for the function f.

g(x)=?

 

[Dick]

The best fit function is clearly g(x)=-3/sqrt(x). But I'm guessing you trying to fit a function that's doesn't have that form. What kind of function are you trying to fit and what's the definition of 'least squares fit'?

 

[tza5021]

Using g(x)= a0+a1x+a2x^2 when 1<x<4
using intergral(f(x)-g(x)dx)

 

[tza5021]

If you could help that would be very much appreciated as I do not knw how to punch and chug that in an intergral.

 

[Dick]

If you could help that would be very much appreciated as I do not knw how to punch and chug that in an intergral.

I think you want to minimize the integral of (f(x)-g(x))^2 don't you? Put in your f(x) and your g(x). It's not a hard integral. Just square it out. It's just powers of x. Then try to minimize with respect to a0, a1 and a2.

 

[tza5021]

How do I minimize the a0,a1 and a2 I do not get that part

 

[Dick]

How do I minimize the a0,a1 and a2 I do not get that part

Use partial derivatives with respect to a0, a1 and a2. What should they be at a minimum? Didn't they teach you that part?

 

[tza5021]

Yes, but I missed the class. So could you tell me how to do that

 

[Dick]

Yes, but I missed the class. So could you tell me how to do that

What should the partial derivatives be at a minimum? Missing the class means i) you could try to find the method yourself by looking it up or reading a book or even better, ii) thinking about it yourself.