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

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JEE Main

IMPORTANT

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If $f (x) = \{\begin{cases} 3 - x^{2}, & x \leq 2 \\ \sqrt{a + 14} - |x - 48|, & x > 2 \end{cases}$ and if $f (x)$ has a local maxima at $x = 2$ , then the greatest value of $a$ is

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Important Questions on Monotonicity and Maxima-Minima of Functions

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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 7

The function

f (x) = x^{5} - 5 x^{4} + 5 x^{3} - 1

has

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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 8

If

f (x) = | x - 1 | + | x - 4 | + | x - 9 | + \dots + | x - 2500 | \forall x \in R

, then set of all the values of

x

, where

f (x)

has minimum values, 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 9

Slope of tangent to the curve

y = 2 e^{x} \sin (\frac{π}{4} - \frac{x}{2}) \cos (\frac{π}{4} - \frac{x}{2})

, is minimum at

x =

(

where

0 \leq x \leq 2 π

)

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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 10

The value of

a

for which all extremum of function

f (x) =

x^{3} - 3 a x^{2} + 3 (a^{2} - 1) x + 1

, lies in the interval

(- 2, 4)

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 11

If the function

f (x) = a x e^{- b x}

has a local maximum at the point

(2, 10)

, then

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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 12

Let

f (x) = \frac{e^{x}}{1 + x^{2}}

and

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

, then

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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 13

If $f^{'} (x) = (x - a)^{2010} (x - b)^{2009}$ and $a > b$ , then

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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 14

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