xx −2−2 11 55 y=f(x)y=f(x) 1414 1717 105105 Hence find: (i) a+b+ca+b+c Answer (ii)f′(1)f′(1) Answer (iii) f′′(3)f″(3) Answer
(a)Use the Lagrange Interpolation Formula to find a polynomial of the form f(x)=ax2+bx+cf(x)=ax2+bx+c that fits all the following values.
| xx | −2−2 | 11 | 55 |
|---|---|---|---|
| y=f(x)y=f(x) | 1414 | 1717 | 105105 |
Hence find:
(i) a+b+ca+b+c Answer
(ii)f′(1)f′(1) Answer
(iii) f′′(3)f″(3) Answer
(b) Obtain the quartic interpolating polynomial of the form f(x)=a+bx+cx2+dx3+ex4f(x)=a+bx+cx2+dx3+ex4 which passes through all the following points.
| xx | 00 | 11 | 22 | 33 | 44 | 55 | 66 |
|---|---|---|---|---|---|---|---|
| y=f(x)y=f(x) | 00 | 44 | 5656 | 264264 | 808808 | 19401940 | 39843984 |
Hence find:
(i) a+b+c+d+ea+b+c+d+e Answer
(ii) a−ba−b Answer
(iii) f(5.5)f(5.5) Answer
(iv) f′(1)f′(1) Answer
(v) f′′(1)f″(1) Answer
(vi) f′′′(1)f‴(1) Answer
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
