Match the given options to fill in the blank. 1. If f' is positive to the left and right of c, then f has ______ at c. 2. If f' is negative to the left and right of c, then f has ______ at c. Options are: a. local maximum b. local minimum c. no local maximum nor minimum

Match the given options to fill in the blank. 1. If f' is positive to the left and right of c, then f has at c. 2. If f' is negative to the left and right of c, then f has at c. Options are: a. local maximum b. local minimum c. no local maximum nor minimum

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

100%

Match the given options to fill in the blank.

1. If f' is positive to the left and right of c, then f has ______ at c.

2. If f' is negative to the left and right of c, then f has ______ at c.

Options are:

a. local maximum

b. local minimum

c. no local maximum nor minimum

Formula Formula A function f(x) attains a local maximum 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 case, f(a) attains a local maximum value f(x) at x=a .

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