5. A curve has equation y + sin 2y = 2x – x². (a) Use implicit differentiation to show that y' = -1 at the point (2,0). (b) Hence, determine y" at the point (2,0). Answer: (c) Use the results of parts (a) and (b) to sketch the curve in the neighbourhood of the point (2,0).

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5. A curve has equation
y3 + sin 2y = 2x – x².
(a) Use implicit differentiation to show that y' = -1 at the point (2,0).
%3D
(b) Hence, determine y" at the point (2,0).
Answer:
(c) Use the results of parts (a) and (b) to sketch the curve in the neighbourhood of
the point (2,0).
Transcribed Image Text:5. A curve has equation y3 + sin 2y = 2x – x². (a) Use implicit differentiation to show that y' = -1 at the point (2,0). %3D (b) Hence, determine y" at the point (2,0). Answer: (c) Use the results of parts (a) and (b) to sketch the curve in the neighbourhood of the point (2,0).
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