Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 12

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Given a function $y = x^{x}, x > 0$ and $0 < x < 1 .$ The values of $x$ for which the function attains the values exceeding to the values of its inverse are:

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Important Questions on Application of Derivatives

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Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 13

P

is a variable point on the curve

y = f (x)

and

A

is a fixed point in the plane not lying on the curve. If

P A^{2}

is minimum, then the angle between

P A

and the tangent at

P

is

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Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 14

Let

f (x) = x^{n + 1} + a \cdot x^{n}

, where

a

and

n

are positive real number. Then,

x = 0

is a point of:

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Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 15

Let

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

and

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

, then

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Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 16

Let

a, b, c, d, e, f, g

and

h

, be distinct elements in the set

\{- 7, - 5, - 3, - 2, 2, 4, 6, 13\}

. Then, the minimum value of

(a + b + c + d)^{2} + (e + f + g + h)^{2}

is:

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Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 17

Minimum integral value of

k

for which the equation

e^{x} = k x^{2}

has exactly three real distinct solutions is:

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Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 18

If

a b = 2 a + 3 b

,

a > 0

,

b > 0

, then the minimum value of

a b

is:

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Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 19

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:

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Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 20

The equation

x^{4} - 2 x^{2} = a

has

4

distinct real roots, then