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    Multivariable calculus

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    Question 1) Find the direction from (-3, 1, 2), in which g(x,y,z)=x^2*y*z-2*z^3 decreases fastest.

    question 2) Follow the line in the direction you found in part 1) to estimate, using linear approximation, the location of the point closest to the coordinates (-3,1,2) at which g=1;Do not use a calculator; Express the answer using fractions. Next, use a calculator to evaluate g at your point.(the value should be reasonably close to 1).

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    1) Find the direction from P(-3, 1, 2), in which g(x,y,z)=x^2*y*z-2*z^3 decreases fastest.
    Solution. Since , we have
    So, we know that the gradient of at P(-3, 1, 2) is

    We know that The direction of grad g(x,y,z) is the direction with maximal directional derivative. The direction of -grad ...

    Solution Summary

    This solution shows how to find the direction from in which a function decreases fastest.