Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 6 - Monotonicity and Maxima-Minima of Functions>DPP>Q 14

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If $\lim_{x \to a} f (x) = \lim_{x \to a} [f (x)]$ , where $[\cdot]$ denotes the greatest integer function and $f (x)$ is a non-constant continuous function, then

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Important Questions on Monotonicity and Maxima-Minima of Functions

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 6 - Monotonicity and Maxima-Minima of Functions>DPP>Q 15

Consider the function

f (x) = \log_{e} (\sqrt{1 - x^{2}} - x)

. Then, which of the following is/are true?

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Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 6 - Monotonicity and Maxima-Minima of Functions>DPP>Q 1

If

f (x) = \{\begin{array}{cl} x^{3} (1 - x), & x \leq 0 \\ x \log_{e} x + 3 x, & x > 0 \end{array}

, then which of the following is not true

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 6 - Monotonicity and Maxima-Minima of Functions>DPP>Q 2

The coordinates of the point on the curve

x^{3} = y (x - a)^{2}

, where the ordinate is minimum is

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JEE Main

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Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 6 - Monotonicity and Maxima-Minima of Functions>DPP>Q 3

The fraction exceeding its

p^{th}

power by the greatest number possible, where

p \geq 2

, is:

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 6 - Monotonicity and Maxima-Minima of Functions>DPP>Q 4

If

f (x) = \{\begin{array}{l} x, & 0 \leq x \leq 1 \\ 2 - e^{x - 1}, & 1 < x \leq 2 \\ x - e, & 2 < x \leq 3 \end{array}\}

and

g^{'} (x) = f (x)

,

x \in [1, 3]

, then:

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 6 - Monotonicity and Maxima-Minima of Functions>DPP>Q 5

If

g (x) = \max (y^{2} - x y)

(where

0 \leq y \leq 1

), then the minimum value of

g (x)

(for real

x

) is:

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 6 - Monotonicity and Maxima-Minima of Functions>DPP>Q 6

If

a, b \in R

distinct numbers satisfying

|a - 1| + |b - 1| = |a| + |b| = |a + 1| + |b + 1|,

then the minimum value of

|a - b|

is:

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 6 - Monotonicity and Maxima-Minima of Functions>DPP>Q 7

If the equation

2 x^{3} - 6 x + 2 \sin a + 3 = 0

, where

a \in (0

,

π)

has only one real root, then the largest interval in which

a

lies is: