Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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The curve defined implicitly by the equation 2x² + xy + 5y? = 30 is shown below.
y
4
-2
-2
-4
dy
(a) Differentiate the curve's equation, to obtain an equation involving x, y, and
dx
(b) Find the coordinates of the curve's stationary points.
(c) Classify the curve's stationary points.
(d) From the graph, it is clear that the curve has four "turning points" in total; two stationary
points and two other points, named more generally as critical points. Briefly explain how
you would find such points, including an equation in your explanation.
2.
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Transcribed Image Text:The curve defined implicitly by the equation 2x² + xy + 5y? = 30 is shown below. y 4 -2 -2 -4 dy (a) Differentiate the curve's equation, to obtain an equation involving x, y, and dx (b) Find the coordinates of the curve's stationary points. (c) Classify the curve's stationary points. (d) From the graph, it is clear that the curve has four "turning points" in total; two stationary points and two other points, named more generally as critical points. Briefly explain how you would find such points, including an equation in your explanation. 2.
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