022 Exam 1 Sample A, Problem 7

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Find the slope of the tangent line to the graph of at the point .

Foundations:  
Recall that for a given value, is precisely the point of the tangent line through the point . Once we have the slope, we can then use the point-slope form for a line:
where is the known slope and is a point on the line.

 Solution:

Finding the slope:  
Note that
so the tangent line through has slope
Write the Equation of the Line:  
Using the point-slope form listed in foundations, along with the point and the slope , we find
or
Final Answer:  

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