Below Is a Graph of Function F(x) $x = a ?$

question 92

Multiple Choice

Below is a graph of function f(x) . Which of the following could be the second Taylor polynomial of f(x) at $x = a ?$

• A) \(\mathrm { P } 2\) (x) = \(\frac { 13 } { 3 }\) + \(\frac { 5 } { 3 }\) (x - a)
• B) \(\mathrm { P } 2\) (x) = \(\frac { 13 } { 3 }\) + \(\frac { 2 } { 3 }\) \(( x - a ) ^ { 2 }\)
• C) \(\mathrm { P } 2\) (x) = \(\frac { 13 } { 3 }\) - \(\frac { 2 } { 3 }\) \(( x - a ) ^ { 2 }\)
• D) \(\mathrm { P } 2\) (x) = \(\frac { 13 } { 3 }\) - \(\frac { 5 } { 3 }\) (x - a) + \(\frac { 2 } { 3 }\) \(( x - a ) ^ { 2 }\)
• E) \(\mathrm { P } 2\) (x) = \(\frac { 5 } { 3 }\) (x - a) - \(\frac { 2 } { 3 }\) \(( x - a ) ^ { 2 }\)

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Definitions:

Output Intensification

A process aimed at increasing the productivity of a system or process, resulting in more output from the same amount of inputs.

Exponential Growth

A pattern of increase where a quantity grows at a rate proportional to its current size, resulting in a rapid escalation over time.

Natural Increase

Population growth measured as the difference between births and deaths in a given population, without considering migration.

Societal Institution

Fundamental social structures and arrangements within a society that order and normalize the behavior of its members.