If a function $$\(f\)$$ is approximated by the third order Taylor series $$\[ 4-3(x-2)+2(x-2)^{2}-7(x-3)^{3} \text { centered at } x=2 \text {, what is } f^{\prime \prime \prime}(2) \text { ? } \]$$

A.
-42
B.
-21
C.
\(-\frac{7}{6}\)
D.
\(\frac{7}{6}\)
Calculus
AP
College Board
Exam No:AP Calculus Unit 10 Questions Set 2 Year:2024 Question No:34

Answer:

A

Knowledge points:

10.11 Finding Taylor Polynomial Approximations of Functions
10.14 Finding Taylor or Maclaurin Series for a Function

Solution:

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