The Data in the Table Report the Average Improvement in Scores

question 3

Essay

The data in the table report the average improvement in scores of six college freshmen who took a writing assessment before and again after they had x hours of tutoring by a tutor trained in a new method of instruction.When f(x)>0 the group showed improvement on average.
$\begin{array}{llllllll}x & 2 & 3.5 & 5 & 6.5 & 8 & 9.5 & 11 \\f(x) & -2 & -1 & 0 & 3 & 7 & 9 & 10\end{array}$
a)Find the average change in score from 6.5 to 9.5 hours of tutoring.
b)Estimate the instantaneous rate of change at 8 hours.
c)Approximate the equation of the tangent line at x = 8 hours.
d)Use the tangent line to estimate f(8.5).

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Definitions:

Intimacy

A close, familiar, and usually affectionate or loving personal relationship with another person.

Isolation

The process or state of being separated from others or the feeling of being alone and unsupported.

Identity Crisis

A period of uncertainty and confusion in which a person's sense of identity becomes insecure, typically due to a change in expected roles or perception of self.

Adolescents

Individuals in the transitional stage of physical and psychological development that typically occurs during the period from puberty to legal adulthood.