Consider f: R R It's true that, O (A) if f is differentiable in a neighbourhood of Xo. then f'(xo) = 0 O (B) if f is differentiable at Xo and f'(xo) = 0, then Xo is a local extremum point of f %3D O (C) if Xo is a local extremum point of f and f is differentiable in Xo, then f'(xo) = 0 O (D) if f is decreasing in R. then f'(x) <0. for all x E R O (E) if Xo is a local extremum point of f and f is differentiable in R\ {Xo}, then f is differentiable at Xo and f'(x) =0 %3D
Consider f: R R It's true that, O (A) if f is differentiable in a neighbourhood of Xo. then f'(xo) = 0 O (B) if f is differentiable at Xo and f'(xo) = 0, then Xo is a local extremum point of f %3D O (C) if Xo is a local extremum point of f and f is differentiable in Xo, then f'(xo) = 0 O (D) if f is decreasing in R. then f'(x) <0. for all x E R O (E) if Xo is a local extremum point of f and f is differentiable in R\ {Xo}, then f is differentiable at Xo and f'(x) =0 %3D
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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Transcribed Image Text:Consider f: R R It's true that,
O (A) if f is differentiable in a neighbourhood of Xo, then f'(Xo) = 0
O (B) if f is differentiable at Xo and f'(xo) = 0, then Xo is a local extremum point of f
O (C) if Xo is a local extremum point of f and f is differentiable in Xo, then f'(xo) = 0
O (D) if f is decreasing in R. then f'(x) < 0, for all x E R
O (E) if Xo is a local extremum point of f and f is differentiable in R\ {xo}, then f is differentiable at Xo and f' (x) = 0
%3D
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