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Vectors and Gradients : Direction of Most Rapid Increase; Critical Points

1. Given f(x,y,z)=x^2y^3z^6, in what direction is F(x,y,z) increasing most rapidly at the point P(1,-1,1). What is the rate of increase?

2. Locate and classify the critical points of the function h(x,y) = x^2 -4x+4xy+y^2-16y.

Solution Summary

Direction of Most Rapid Increase and Critical Points are investigated. The solution is detailed and well presented.