Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 8 - Monotonicity, Maxima and Minima>Proficiency in 'Monotonicity, Maxima and Minima' Exercise 1>Q 26

EASY

JEE Main

IMPORTANT

Earn 100

Analyze the following graph of $f^{'} (x)$ :

Which is incorrect about $f (x)$ for $α < x < β$ $?$

33.33% studentsanswered this correctly

Important Questions on Monotonicity, Maxima and Minima

HARD

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 8 - Monotonicity, Maxima and Minima>Proficiency in 'Monotonicity, Maxima and Minima' Exercise 1>Q 27

Let

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

and

g (x) = f (f (x) - 1) + f (5 - f (x))

, then

MEDIUM

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 8 - Monotonicity, Maxima and Minima>Proficiency in 'Monotonicity, Maxima and Minima' Exercise 1>Q 28

Let

f : N \to N

be such that

f (n + 1) > f (f (n))

for all

n \in N

, then

HARD

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 8 - Monotonicity, Maxima and Minima>Proficiency in 'Monotonicity, Maxima and Minima' Exercise 1>Q 29

The equation

|2 a x - 3| + |a x + 1| + |5 - a x| = \frac{1}{2}

possesses

HARD

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 8 - Monotonicity, Maxima and Minima>Proficiency in 'Monotonicity, Maxima and Minima' Exercise 1>Q 30

Which of the following is/are true? (you may use

f (x) = \frac{\ln (l n x)}{l n x}

)

MEDIUM

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 8 - Monotonicity, Maxima and Minima>Proficiency in 'Monotonicity, Maxima and Minima' Exercise 1>Q 31

If

\underset{x \to a}{l i m} f (x) = \underset{x \to a}{l i m} [f (x)]

(

[\cdot]

denotes the greatest integer function) and

f (x)

is non-constant continuous function, then

MEDIUM

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 8 - Monotonicity, Maxima and Minima>Proficiency in 'Monotonicity, Maxima and Minima' Exercise 1>Q 32

Let

S

be the set of real values of parameter

λ

for which the equation

f (x) = 2 x^{3} - 3 (2 + λ) x^{2} + 12 λ x

has exactly one local maximum and exactly one local minimum. Then,

S

is a subset of

HARD

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 8 - Monotonicity, Maxima and Minima>Proficiency in 'Monotonicity, Maxima and Minima' Exercise 1>Q 33

h (x) = 3 f (\frac{x^{2}}{3}) + f (3 - x^{2}), \forall x \in (- 3, 4)

, where

f^{''} (x) > 0, \forall x \in (- 3, 4)

, then

h (x)

is

HARD

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 8 - Monotonicity, Maxima and Minima>Proficiency in 'Monotonicity, Maxima and Minima' Exercise 1>Q 34

Let

f (x) = l n (2 x - x^{2}) + s i n \frac{π x}{2}

. Then,