The equation of a curve C is given by y3 + y = x* + a° + 8. (a) Using implicit differentiation, find the slope of the curve at the point P(1,2). (b) Determine y" at P.

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2. The equation of a curve C is given by
y3 +y = x* + a° + 8.
(a) Using implicit differentiation, find the slope of the curve at the point P(1,2).
(b) Determine y" at P.
(c) Sketch the curve C in the neigh-
P.
bourhood of P.
(Hint: Use the values of y and y"
obtained in parts (a) and (b) above.)
Transcribed Image Text:2. The equation of a curve C is given by y3 +y = x* + a° + 8. (a) Using implicit differentiation, find the slope of the curve at the point P(1,2). (b) Determine y" at P. (c) Sketch the curve C in the neigh- P. bourhood of P. (Hint: Use the values of y and y" obtained in parts (a) and (b) above.)
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