Suppose a Function Satisfies $f(5)=2$ $f^{\prime}(5)=5$ $f^{\prime \prime}(5)=-7$ , And $f^{\prime \prime \prime}$

Multiple Choice

Suppose a function satisfies $f(5) =2$ , $f^{\prime}(5) =5$ , $f^{\prime \prime}(5) =-7$ , and $f^{\prime \prime \prime}$$(5) =12$ .What is the third degree Taylor polynomial for f about x = 5?

A) $2+5(x-5) -7(x-5) ^{2}+12(x-5) ^{3}$
B) $2+5(x-5) -\frac{7}{2}(x-5) ^{2}+2(x-5) ^{3}$
C) $2+5 x-\frac{7}{2} x^{2}+2 x^{3}$
D) $10+25 x-\frac{35}{2} x^{2}+6 x^{3}$