Consider the following equation: F(x, y, z) = (x + 9)23 +sin(y)+25+2=0 Assume a point (ro,...

 

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Consider the following equation: F(x, y, z) = (x² + 9)23 +sin(y)+25+2=0 Assume a point (ro, yo, zo) satisfies this equation. What are the possibilities of the values of zo and yo for which the given equation defines an implicit function z = 2(x, y) such that F(x, y, z(x, y)) = 0 on a neighbourhood of (ro. 3o)? Find all critical points (k. Yk) of z(x, y). Consider the following equation: F(x, y, z) = (x² + 9)23 +sin(y)+25+2=0 Assume a point (ro, yo, zo) satisfies this equation. What are the possibilities of the values of zo and yo for which the given equation defines an implicit function z = 2(x, y) such that F(x, y, z(x, y)) = 0 on a neighbourhood of (ro. 3o)? Find all critical points (k. Yk) of z(x, y).