Beta Question Bank for Engineering: Mathematics>Chapter 27 - Continuity and Differentiability>EXERCISE-1>Q 26

HARD

JEE Main/Advance

IMPORTANT

Earn 100

Rolle's theorem in the indicated intervals will not be valid for which of the following function

50% studentsanswered this correctly

Important Questions on Continuity and Differentiability

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 27 - Continuity and Differentiability>EXERCISE-1>Q 27

Consider the function for

x \in [- 2, 3], f (x) = \{\begin{matrix} \frac{x^{3} - 2 x^{2} - 5 x + 6}{x - 1}, & x \neq 1 \\ - 6, & x = 1 \end{matrix}\}

, then

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 27 - Continuity and Differentiability>EXERCISE-1>Q 28

If the function

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

satisfies LMVT at

x = 2

on the closed interval

[1, a]

then the value of

' a'

is equal to

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 27 - Continuity and Differentiability>EXERCISE-1>Q 29

Consider the function

f (x) = 8 x^{2} - 7 x + 5

on the interval

[- 6, 6]

. The value of

c

that satisfies the conclusion of the mean value theorem, is

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 27 - Continuity and Differentiability>EXERCISE-1>Q 30

Let

f

be a function which is continuous and differentiable for all real

x

. If

f (2) = - 4

and

f^{'} (x) \geq 6

for all

x \in [2, 4]

, then

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 27 - Continuity and Differentiability>EXERCISE-1>Q 31

If

f (x) = x^{3} + 7 x - 1

, then

f (x)

has a zero between

x = 0

and

x = 1

. The theorem that best describes this is:

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 27 - Continuity and Differentiability>EXERCISE-1>Q 32

Consider

f (x) = | 1 - x |, 1 \leq x \leq 2

and

g (x) = f (x) + b \sin (\frac{π}{2} x), 1 \leq x \leq 2,

then which of the following is correct?

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 27 - Continuity and Differentiability>EXERCISE-2>Q 1

Consider the piecewise defined function

f (x) = [\begin{matrix} \sqrt{- x} & if x < 0 \\ 0 & if 0 \leq x \leq 4 \\ x - 4 & if x > 4 \end{matrix}

choose the answer which best describes the continuity of this function-

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 27 - Continuity and Differentiability>EXERCISE-2>Q 2

f (x)

is continuous at

x = 0

, then which of the following are always true?