Examine if Rolle's theorem is applicable to any of the following functions. Can you say something about the converse of Rolle's theorem from these example?
(i) $f (x) = [x]$ for $x \in [5, 9]$
(ii) $f (x) = [x]$ for $x \in [- 2, 2]$
(iii) $f (x) = x^{2} - 1$ for $x \in [1, 2]$

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Examine if Rolle's theorem is applicable to any of the following functions. Can you say something about the converse of Rolle's theorem from these example?
(i)

f (x) = [x]

for

x \in [5, 9]

(ii)

f (x) = [x]

for

x \in [- 2, 2]

(iii)

f (x) = x^{2} - 1

for

x \in [1, 2]

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Question Text

Examine if Rolle's theorem is applicable to any of the following functions. Can you say something about the converse of Rolle's theorem from these example?
(i)

f (x) = [x]

for

x \in [5, 9]

(ii)

f (x) = [x]

for

x \in [- 2, 2]

(iii)

f (x) = x^{2} - 1

for

x \in [1, 2]

Examine if Rolle's theorem is applicable to any of the following functions. Can you say something about the converse of Rolle's theorem from these example?
(i) $f (x) = [x]$ for $x \in [5, 9]$
(ii) $f (x) = [x]$ for $x \in [- 2, 2]$
(iii) $f (x) = x^{2} - 1$ for $x \in [1, 2]$

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Examine if Rolle's theorem is applicable to any of the following functions. Can you say something about the converse of Rolle's theorem from these example?(i) f(x)=[x] for x∈[5,9](ii) f(x)=[x] for x∈[−2,2](iii) f(x)=x2−1 for x∈[1,2]

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Practice questions from similar books

Examine if Rolle's theorem is applicable to any of the following functions. Can you say something about the converse of Rolle's theorem from these example?
(i) $f (x) = [x]$ for $x \in [5, 9]$
(ii) $f (x) = [x]$ for $x \in [- 2, 2]$
(iii) $f (x) = x^{2} - 1$ for $x \in [1, 2]$