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If f'(x) has no roots, then f (x) has exactly one root. If f (x) has three roots, then f'(x) has at least two roots. f (x) always has more roots than f'(x). f (x) and f'(x) cannot share the same roots.

If f'(x) has no roots, then f (x) has exactly one root. If f (x) has three roots, then f'(x) has at least two roots. f (x) always has more roots than f'(x). f (x) and f'(x) cannot share the same roots.

Calculus: Early Transcendentals
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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If f'(x) has no roots, then f (x ) has exactly one root. If f (x) has three roots, then f'(x) has at least two roots. f (x) always has more roots than f'(x). f (x) and f'(x) cannot share the same roots.
Transcribed Image Text:If f'(x) has no roots, then f (x ) has exactly one root. If f (x) has three roots, then f'(x) has at least two roots. f (x) always has more roots than f'(x). f (x) and f'(x) cannot share the same roots.
Let f(x) be a differentiable function whose domain is all real numbers. Select all statements which must be true.
Transcribed Image Text:Let f(x) be a differentiable function whose domain is all real numbers. Select all statements which must be true.
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