Concept explainers
(a)
To find: the slope of the graph at the given point
(a)
Answer to Problem 47E
The slope of the graph is
Explanation of Solution
Given:
Calculation:
In order to find the slope of the graph at the point
Therefore, using the given function
Conclusion:
(b)
To find: an equation of the tangent line
(b)
Answer to Problem 47E
An equation of the tangent line is
Explanation of Solution
Calculation:
The slope m of the graph at this point that obtained in part (a) is also the slope of the tangent line to the graph at this point. Therefore, simply plug this slope, and the given point into the equation
Conclusion:
An equation of the tangent line is
(c)
To graph: the function and the tangent line.
(c)
Answer to Problem 47E
Explanation of Solution
Calculation:
Now, graph the given function and the equation of the tangent line just found in the same viewing window:
Conclusion:
Thus, the required graph is drawn.
Chapter 11 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
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