Mathematics Crash Course JEE Main>Chapter 1 - Application of Derivatives>Level 2>Q 24

HARD

JEE Main

IMPORTANT

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The global maxima and global minima of $f (x) = \frac{e^{x} + e^{- x}}{2}$ , when $x \in [- \log_{e} 2, \log_{e} 7]$ are respectively.

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Important Questions on Application of Derivatives

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 1 - Application of Derivatives>Level 2>Q 25

The value of

' a'

for which the function

f (x) = x^{3} + 3 (a - 7) x^{2} + 3 (a^{2} - 9) x - 2

has a positive point of maxima, is:

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 1 - Application of Derivatives>Level 2>Q 26

Let

p (x)

be a real polynomial of least degree which has a local maximum at

x = 1

and a local minimum at

x = 3

. If

p (1) = 6

and

p (3) = 2

, then

p^{'} (0)

is

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 1 - Application of Derivatives>Level 2>Q 27

A running track of

440 ft

is to be laid out enclosing a football field, the shape of which is a rectangle with a semicircle at each end. If the area of rectangular portion is to be maximum, then lengths of sides are

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 1 - Application of Derivatives>Level 2>Q 28

If the sum of length of the hypotenuse and another side of a right-angled triangle is given. The area of the triangle is maximum when the angle between them is

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 1 - Application of Derivatives>Level 2>Q 29

A wire of length

2

units is cut into two parts which are bent respectively to form a square of side

= x

units and a circle of radius

= r

units. If the sum of the areas of the square and the circle so formed is minimum, then

MEDIUM

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 1 - Application of Derivatives>Level 2>Q 30

We have three real roots of cubic equation

x^{3} - p x + q

, where

p > 0

and

q > 0

, then which of the below given statement is correct?

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 1 - Application of Derivatives>Level 2>Q 31

The total number of local maxima and local minima of the function

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

is equal to

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 1 - Application of Derivatives>Level 2>Q 32

Maximum value of a function

f (x) = {(\frac{1}{x})}^{x}

is

(p)^{q}

. Then, the value of

[p] + [\frac{1}{q}]

, where

[\cdot]

represents the greatest integer function, is