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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

Let f ( x ) = tan x . Show that f ( 0 ) = f ( π ) but there is no number c in ( 0 , π ) such that f′(c) = 0. Why does this not contradict Rolle’s Theorem?

To determine

To show:

f0=f(π) but there is no number c in (0, π) such that f'c=0 and

explain why does this not contradict the Rolle’s theorem

Explanation

1) Concept:

Using the Rolle’s Theorem verify the result

2) Theorem:

Rolle’s Theorem – Let f  be a function that satisfies the following 3 hypotheses:

i. f is continuous on the closed interval [a, b]

ii. f is differentiable on the open interval (a, b)

iii. f (a)=f (b)

Then there is a number c in (a, b) such that f'c=0

3) Given:

fx=tanx

4) Calculation:

f0=fπ=0 but function is not continuous in the interval (0, π) since,f(π2) not defined

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