RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 10 - Rolle's Theorem and Lagrange's Mean Value Theorem>EXERCISE>Q 1

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12th West Bengal Board

IMPORTANT

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The conclusion of Rolle's theorem holds at the point $x =$ , when it is applied on $x^{2} - x - 12$ in $[- 3, 4]$ .

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Important Questions on Rolle's Theorem and Lagrange's Mean Value Theorem

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12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 10 - Rolle's Theorem and Lagrange's Mean Value Theorem>EXERCISE>Q 1

The Rolle's theorem is _____ (applicable / not applicable) to

f (x) = \sqrt{x}

in

[- 1, 1]

.

EASY

12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 10 - Rolle's Theorem and Lagrange's Mean Value Theorem>EXERCISE>Q 1

The Rolle's theorem is _____ (applicable / not applicable) to

f (x) = [x]

in

[- 3, 3]

.

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12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 10 - Rolle's Theorem and Lagrange's Mean Value Theorem>EXERCISE>Q 1

The value of

c \in (\frac{1}{2}, 3)

is

x =

_____ when Rolle's theorem is applied on

f (x) = 2 x^{3} - 5 x^{2} - 4 x + 3

in

[\frac{1}{2}, 3]

.

EASY

12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 10 - Rolle's Theorem and Lagrange's Mean Value Theorem>EXERCISE>Q 2

Rolle's theorem is always applicable to any continuous function

y = f (x)

in

[a, b]

for which

f (a) = f (b)

holds.

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12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 10 - Rolle's Theorem and Lagrange's Mean Value Theorem>EXERCISE>Q 2

Conclusion of the Rolle's theorem may be true for a function

f

in

[a, b]

, though all the conditions of the theorem are not satisfied by

f

on

[a, b]

.

EASY

12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 10 - Rolle's Theorem and Lagrange's Mean Value Theorem>EXERCISE>Q 2

If at least one condition of Rolle's theorem is not satisfied by a function

f

on

[a, b]

, then

f^{'} (c) \neq 0

for any

c \in (a, b)

.

EASY

12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 10 - Rolle's Theorem and Lagrange's Mean Value Theorem>EXERCISE>Q 2

Rolle's theorem is applicable to

f (x) = \tan x

in

[0, π]

.

EASY

12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 10 - Rolle's Theorem and Lagrange's Mean Value Theorem>EXERCISE>Q 2

Rolle's theorem is applicable to

f (x) = x^{\frac{2}{3}}

in

[- 1, 1]

.