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:

Pharyngeal Pouches

Embryonic features that form structures of the face and neck in vertebrates.

Evolution

The process by which different kinds of living organisms are thought to have developed and diversified from earlier forms during the history of the earth.

Chordate Features

Distinctive characteristics of the Chordata phylum, including a notochord, a dorsal hollow nerve cord, pharyngeal slits, and a post-anal tail, at some stage of development.

Amnion

Extraembryonic membrane of birds, reptiles, and mammals that forms an enclosing, fluid-filled sac.