Suppose f'(x0) = 0, f" (x0) = 0, ..., f(n-1)(xo) = 0 and f(m) (xo) >0, for a Cn function f. Prove that f has a local minimum at zoif n is even and that xo is neither a local maximum nor a localminimum if n is odd.

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Suppose f'(xo) = 0, f" (xo) = 0, .…, f(n-1)(xo) = 0 and f(") (xo) > 0, for a C function f. Prove that f has a local minimum at ro if n is even and that xo is neither a local maximum nor a local minimum if n is odd.

Suppose f'(xo) = 0, f" (xo) = 0, .…, f(n-1)(xo) = 0 and f(") (xo) > 0, for a C function f. Prove that f has a local minimum at ro if n is even and that xo is neither a local maximum nor a local minimum if n is odd.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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Question

Suppose f'(x0) = 0, f" (x0) = 0, ..., f(n-1)(xo) = 0 and f(m) (xo) >
0, for a Cn function f. Prove that f has a local minimum at zo
if n is even and that xo is neither a local maximum nor a local
minimum if n is odd.

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