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Let f(x, y) = ln (1 + x² + y²), then a) f is not differentiable at (0,0). b) f(xo, yo) = f(xo, yo) for any points (xo, yo). c) # 2² əxdy d) the gradient Vƒ(1, 1) at the point (1,1) is orthogonal to the vector (1, 2)T. 0² f əyəx at a point (x, y). e) Exists a point (xo, yo) such that the gradient Vf(xo, yo) at that point is the null vector.

Let f(x, y) = ln (1 + x² + y²), then a) f is not differentiable at (0,0). b) f(xo, yo) = f(xo, yo) for any points (xo, yo). c) # 2² əxdy d) the gradient Vƒ(1, 1) at the point (1,1) is orthogonal to the vector (1, 2)T. 0² f əyəx at a point (x, y). e) Exists a point (xo, yo) such that the gradient Vf(xo, yo) at that point is the null vector.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let f(x, y) = ln (1 + x² + y²), then a) f is not differentiable at (0,0). af b) (xo, yo) af dx (xo, yo) for any points (xo, yo). მყ c) 0² f a² f # əxəy əyəx d) the gradient Vƒ(1, 1) at the point (1,1) is orthogonal to the vector (1,2)T. = at a point (x, y). e) Exists a point (xo, yo) such that the gradient Vf(xo, yo) at that point is the null vector.
Transcribed Image Text:Let f(x, y) = ln (1 + x² + y²), then a) f is not differentiable at (0,0). af b) (xo, yo) af dx (xo, yo) for any points (xo, yo). მყ c) 0² f a² f # əxəy əyəx d) the gradient Vƒ(1, 1) at the point (1,1) is orthogonal to the vector (1,2)T. = at a point (x, y). e) Exists a point (xo, yo) such that the gradient Vf(xo, yo) at that point is the null vector.
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