Find the coefficient of $( x - 2 ) ^ { 2 }$ in the Taylor polynomial $T _ { 2 } ( x )$ for the function $x ^ { 3 }$ at the number 2.
A)3
B)0
C)1
D)6
E)2
F)5
G)8
H)4

Question

Quizplus · Accepted Answer

The Taylor polynomial $T_2(x)$ for $x^3$ at $x=2$ is derived from the expansion of $x^3$ around 2. The second derivative of $x^3$ is $6x$, and evaluated at $x=2$, it gives 12. Dividing by 2! gives the coefficient of $(x-2)^2$ as 6.

Find the Coefficient Of (x−2)2( x - 2 ) ^ { 2 }(x−2)2

Find the Coefficient Of $( x - 2 ) ^ { 2 }$