Is f(x, y) = (x^2)(y^3) + xy^2 − 3x^2 + 4y^2 − 5 differentiable everywhere? Justify your answer. (b) If f is differentiable at P(−1, 1, −4), then find the local linear approximation to f at P. Simplify your answer

Is f(x, y) = (x^2)(y^3) + xy^2 − 3x^2 + 4y^2 − 5 differentiable everywhere? Justify your answer. (b) If f is differentiable at P(−1, 1, −4), then find the local linear approximation to f at P. Simplify your answer

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

ChapterA: Appendix

SectionA.2: Geometric Constructions

Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...

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Question

(a) Is f(x, y) = (x^2)(y^3) + xy^2 − 3x^2 + 4y^2 − 5 differentiable everywhere? Justify your answer.
(b) If f is differentiable at P(−1, 1, −4), then find the local linear approximation
to f at P. Simplify your answer

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