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

question 31

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

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Definitions:

Demand Function

A mathematical expression showing the relationship between the quantity demanded of a good and its price, along with other determinants like income and prices of related goods.

Substitution Effect

The change in consumption patterns due to a change in the relative prices of goods, leading consumers to substitute one good for another.

Income

The money received by an individual or entity, typically measured over a certain period, for labor, services, or through investments.

Claret

A term primarily used in British English to refer to red Bordeaux wine.