Let $$\(h\)$$ be a function for which all derivatives exist at $$\(x=1\)$$. If $$\(h(1)\)$$ $$\(=h^{\prime}(1)=h^{\prime \prime}(1)=h^{\prime \prime \prime}(1)=6\)$$, which third-degree polynomial best approximates $$\(h\)$$ there?
A.
\(6+6 x+6 x^{2}+6 x^{3}\)
B.
\(6+6(x-1)+6(x-1)^{2}+6(x-1)^{3}\)
C.
\(6+6 x+3 x^{2}+x^{3}\)
D.
\(6+6(x-1)+3(x-1)^{2}+(x-1)^{3}\)
Exam No：AP Calculus Unit 10 Questions Set Year：2024 Question No：38
Answer:
D
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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