Let & be continuous in [a,b] and differentiable in (a,b). It's true that: a) f (a) = f(b) = 3 x € (a,b) such that the tangent line to the graph of at (nor f(no)) is horizontal. b) there exists - (b) c) f(a) > f (b) f is decreasing in (a,b) d) fla) 0, \₂ € (a, b)

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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Let & be continuous in [a,b] and differentiable in (a,b). It's true that:
a) f (a) = f(b) = 3 x € (a,b) such that the tangent line to the graph of at (nor f(no))
is horizontal.
b) there exists - (b)
c) f(a) > f (b) f is decreasing in (a,b)
d) fla)
<f(b) f([a,b]) =[f(a), f(b)]
e) f is strictly increasing in (a,b) ⇒ f'(x) >0, \₂ € (a, b)
Transcribed Image Text:Let & be continuous in [a,b] and differentiable in (a,b). It's true that: a) f (a) = f(b) = 3 x € (a,b) such that the tangent line to the graph of at (nor f(no)) is horizontal. b) there exists - (b) c) f(a) > f (b) f is decreasing in (a,b) d) fla) <f(b) f([a,b]) =[f(a), f(b)] e) f is strictly increasing in (a,b) ⇒ f'(x) >0, \₂ € (a, b)
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