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Analyzing critical points Find the critical
Chapter 13, Problem 17E(choose chapter or problem)
Analyzing critical points Find the critical points of the following functions. Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum, local minimum, or saddle point. Confirm your results using a graphing utility
\(f(x, y)=-4 x^{2}+8 y^{2}-3\)
Questions & Answers
QUESTION:
Analyzing critical points Find the critical points of the following functions. Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum, local minimum, or saddle point. Confirm your results using a graphing utility
\(f(x, y)=-4 x^{2}+8 y^{2}-3\)
ANSWER:Solution 17EStep 1 of 3: Critical point : A critical point of a function with two variables is a point where the partial derivatives of first order are equal to zero.Saddle point : A point is a saddle point of a function of two variables if Second Derivative test : The second partial derivatives of f are continuous throughout an interval centered at the point (a , b) where and 1. If , then f has local maximum value at (a , b) .2. If , then f has local minimum value at (a , b) .3. If , then f has a saddle point at (a , b) .4. If , then the test is inconclusive.