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Vector Calculus

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F(x,y) = x^3 + y - xy + 1

a) Are there points on the curve y = (x - 1)^2 where Gradient f is perpendicular to the curve?

b) Find the absolute maximum and minimum of the function in the region 1 >= x >= 0 and y >= 0.

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Solution Summary

A vector function is analyzed. The absolute maximum and minimum of a function in the region is determined. The solution is detailed and well presented.

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a) Gradient of the function f(x,y) = x^3 + y - xy + 1 has components:
3x^2 - y and 1-x. A normal vector to the curve y = (x - 1)^2 has components 2(x-1) and -1. ...

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