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Let f(x, y) = ln (1 + x² + y²), then a) f is not differentiable at (0, 0). b) Exists a point (xo, yo) such that the gradient Vf(xo, yo) at that point is the null vector. c) of (xo, yo) = f(xo, yo) for any points (ro, yo). 2² f a² f d) # Əxdy дудх e) the gradient Vf(1, 1) at the point (1, 1) is orthogonal to the vector (2, 1)T. at a point (x, y).

Let f(x, y) = ln (1 + x² + y²), then a) f is not differentiable at (0, 0). b) Exists a point (xo, yo) such that the gradient Vf(xo, yo) at that point is the null vector. c) of (xo, yo) = f(xo, yo) for any points (ro, yo). 2² f a² f d) # Əxdy дудх e) the gradient Vf(1, 1) at the point (1, 1) is orthogonal to the vector (2, 1)T. at a point (x, y).

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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Which option is right? Can you explain all the falses are why false?

a) f is not differentiable at (0, 0). b) Exists a point (xo, yo) such that the gradient Vf(xo, yo) at that point is the null vector. af əx Let f(x, y) = ln (1 + x² + y²), then c) (xo, yo) = 8² f af (xo, yo) for any points (ro, yo). f y byde # at a point (x, y). əyəx d) дхду e) the gradient Vƒ(1, 1) at the point (1, 1) is orthogonal to the vector (2,1)T.
Transcribed Image Text:a) f is not differentiable at (0, 0). b) Exists a point (xo, yo) such that the gradient Vf(xo, yo) at that point is the null vector. af əx Let f(x, y) = ln (1 + x² + y²), then c) (xo, yo) = 8² f af (xo, yo) for any points (ro, yo). f y byde # at a point (x, y). əyəx d) дхду e) the gradient Vƒ(1, 1) at the point (1, 1) is orthogonal to the vector (2,1)T.
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