Let the function f(x) be a cubic polynomial of the form ax^3+bx^2+cx +d, and it satisfy the constraints f(0) = 7, f(1) = 10, f(2) = 15 and f(3) = 28. Compute a+2b+3c+4d.
+128460 If f(0) = 7.....then d = 7
And we have this system
a + b + c + 7 = 10 ⇒ a + b + c = 3
8a + 4b + 2c + 7 = 15 ⇒ 8a + 4b + 2c = 8
27a + 9b + 3c + 7 = 28 ⇒ 27a + 9b + 3c = 21
Multiplying the first equation by -2 and adding to the second gives us
6a + 2b = 2 (4)
Multiplying the first equation by - 3 and adding to the third produces
24a + 6b = 12 (5)
Mutiply ( 4) by -3 and add to (5) and we get that
6a = 6
a = 1
6(1) + 2b = 2
2b = -4
b = -2
1 - 2 + c = 3
-1 + c = 3
c = 4
a + 2b + 3c + 4d =
1 - 4 + 12 + 28 =
37
