23-26 True-False Determine whether the statement is true or false. Explain your answer. In these exercises, assume that f(x, y) has continuous second-order partial derivatives and that D(x, y) = fxx(x, y)fyy(x, y) – f,(x, y) 23. If the function f is defined on the disk x² + y² < 1, then f has a critical point somewhere on this disk. 24. If the function f is defined on the disk x² + y? < 1, and if f is not a constant function, then f has a finite number of critical points on this disk. %3D 25. If P(xo, yo) is a critical point of f, and if f is defined on a disk centered at P with D(xo, yo) > 0, then f has a relative extremum at P
23-26 True-False Determine whether the statement is true or false. Explain your answer. In these exercises, assume that f(x, y) has continuous second-order partial derivatives and that D(x, y) = fxx(x, y)fyy(x, y) – f,(x, y) 23. If the function f is defined on the disk x² + y² < 1, then f has a critical point somewhere on this disk. 24. If the function f is defined on the disk x² + y? < 1, and if f is not a constant function, then f has a finite number of critical points on this disk. %3D 25. If P(xo, yo) is a critical point of f, and if f is defined on a disk centered at P with D(xo, yo) > 0, then f has a relative extremum at P
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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