Image attached shows the graph of the derivative of a continuous function g. a) List the critical numbers of g b) What values of x result in a local maximum c) What values of x result in a local minimum

Image attached shows the graph of the derivative of a continuous function g. a) List the critical numbers of g b) What values of x result in a local maximum c) What values of x result in a local minimum

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.7: Applications

Problem 13EQ

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Question

Image attached shows the graph of the derivative of a continuous function g.
a) List the critical numbers of g
b) What values of x result in a local maximum
c) What values of x result in a local minimum

Formula Formula A function f ( x ) is also said to have attained a local minimum at x = a , if there exists a neighborhood ( a − δ , a + δ ) of a such that, f ( x ) > f ( a ) , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a f ( x ) − f ( a ) > 0 , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a In such a case f ( a ) is called the local minimum value of f ( x ) at x = a .

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