Use a truncated Taylor series expansion, estimate the value of f(3)?

0 ⤊

For an unknown function f(x).
f(2)=8
f'(2)=7
f"(2)=6

2007-02-09 04:40:38 · 3 answers · asked by ksmog00 1 in Science & Mathematics ➔ Mathematics

f(3) = f(2) + f'(2)(3-2) + 1/2 f''(2) (3-2)^2 +....
so

f(3) = 8 + 7 + 1/2 6 +.... = 18 + ....

2007-02-09 04:47:52 · answer #1 · answered by Theta40 7 · 0⤊ 0⤋

f(x) = 8 +7(x-2)+6/2 *(x-2)^2 We must stop here becaus there is no more information
So f(3) =8 +7 +3*1^2 =18

2007-02-09 13:34:21 · answer #2 · answered by santmann2002 7 · 0⤊ 0⤋

f(x) = f(2) + f'(2)(x-2)/1! + f"(2)(x-2)^2/2!
now substitute respective values for all the derivatives and 3 for x.

2007-02-09 12:57:55 · answer #3 · answered by san 3 · 0⤊ 0⤋