(a)
To find: The slope of the folium of Descartes at the given points.
(a)
Answer to Problem 55E
The slope at the point
The slope at the point
Explanation of Solution
Given Information: The equation of the folium of Descartes is
Calculation:
The slope of the folium of Descartes
The slope at the point
The slope at the point
Conclusion:
The slope at the point
The slope at the point
(b)
To calculate: Thepoint other than the origin does the folium have a horizontal tangent.
(b)
Answer to Problem 55E
The coordinate other than origin is
Explanation of Solution
Given Information: The equation of the folium of Descartes is
Calculation:
The folium of Descartes has a horizontal tangent when
The value of
Equate the derivative to 0,
Substitute
Since
Hence, the coordinate other than origin is
Conclusion:
The coordinate other than origin is
(c)
To calculate: Thefolium have a vertical tangent.
(c)
Answer to Problem 55E
The coordinate other than origin is
Explanation of Solution
Given Information: The equation of the folium of Descartes is
Calculation:
The folium of Descartes has a vertical tangent when
The value of
Equate the derivative to 0,
Substitute
Since
Hence, the coordinate other than origin is
Conclusion:
The coordinate other than origin is
Chapter 4 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
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