MATHEMATICS CLASS XII VOLUME-1>Chapter 17 - Increasing and Decreasing Functions>EXERCISE>Q 31

EASY

12th CBSE

IMPORTANT

Earn 100

Prove that the function $f$ given by $f (x) = x^{3} - 3 x^{2} + 4 x$ is strictly increasing on $R$ ?

Important Questions on Increasing and Decreasing Functions

EASY

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-1>Chapter 17 - Increasing and Decreasing Functions>EXERCISE>Q 32

Prove that the function

f (x) = \cos (x)

strictly decreasing in

(0, π)

.

EASY

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-1>Chapter 17 - Increasing and Decreasing Functions>EXERCISE>Q 33

Prove that the function

f (x) = \cos (x)

strictly increasing in

(π, 2 π)

.

EASY

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-1>Chapter 17 - Increasing and Decreasing Functions>EXERCISE>Q 33

Prove that the function

f (x) = \cos (x)

is neither increasing nor decreasing in

(0, 2 π)

.

MEDIUM

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-1>Chapter 17 - Increasing and Decreasing Functions>EXERCISE>Q 33

Show that

f (x) = x^{2} - x \sin x

is an increasing function on

(0, \frac{π}{2})

?

MEDIUM

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-1>Chapter 17 - Increasing and Decreasing Functions>EXERCISE>Q 34

Find the value(s) of

a

for which

f (x) = x^{3} - ax

is an increasing function on

R

?

EASY

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-1>Chapter 17 - Increasing and Decreasing Functions>EXERCISE>Q 35

Find the value of

b

for which the function

f (x) = \sin x - b x + c

is decreasing function on

R .

MEDIUM

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-1>Chapter 17 - Increasing and Decreasing Functions>EXERCISE>Q 37

Show that

f (x) = x + \cos x - a

is an increasing function on

ℝ

for all values of

a

?

HARD

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-1>Chapter 17 - Increasing and Decreasing Functions>EXERCISE>Q 38

Let

f

defined on

[0, 1]

be twice differentiable such that

| f'' (x) | \leq 1 for all x \in [0, 1]

. If

f (0) = f (1)

, then show that

| f' (x) | < 1 for all x \in [0, 1]

.