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) $10+25 x-\frac{35}{2} x^{2}+6 x^{3}$

Question

Quizplus · Accepted Answer

The third degree Taylor polynomial for a function $f$ about $x = 5$ is given by $f(5) + f'(5)(x-5) + \frac{f''(5)}{2}(x-5)^2 + \frac{f'''(5)}{6}(x-5)^3$. Substituting the given values, we get $2 + 5(x-5) - \frac{7}{2}(x-5)^2 + 2(x-5)^3$.

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

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