Let f(x, y) be a function with continuous second partial derivatives. If f. (x, y) = x + 3y and f,(x, y) = 9y² + 3x, which of the following statements is true about f at (-3, 1)? O (-3, 1) is not a critical point of f. O f has a local maximum at (-3, 1). O f has a local minimum at (-3, 1). O (-3, 1) is a saddle point of f.

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Let f(x, y) be a function with continuous second partial derivatives. If fz (x, y) = x + 3y
and f,(x, y) = 9y² + 3x, which of the following statements is true about f at (-3, 1)?
O (-3, 1) is not a critical point of f.
O f has a local maximum at (-3, 1).
O f has a local minimum at (-3, 1).
O (-3, 1) is a saddle point of f.
Transcribed Image Text:Let f(x, y) be a function with continuous second partial derivatives. If fz (x, y) = x + 3y and f,(x, y) = 9y² + 3x, which of the following statements is true about f at (-3, 1)? O (-3, 1) is not a critical point of f. O f has a local maximum at (-3, 1). O f has a local minimum at (-3, 1). O (-3, 1) is a saddle point of f.
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