Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 36

HARD

Mathematics

IMPORTANT

Earn 100

Let $f (x) = l n (2 x - x^{2}) + s i n \frac{π x}{2}$ . Then,

50% studentsanswered this correctly

Important Questions on Application of Derivatives

HARD

Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 37

Let

f (x) = a b s i n x + b \sqrt{1 - a^{2}} c o s x + c

, where

|a| < 1, b > 0,

then

HARD

Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 38

f (x) = \sqrt{x - 1} + \sqrt{2 - x}

and

g (x) = x^{2} + b x + c

are two given functions such that

f (x)

and

g (x)

attain their maximum and minimum values respectively for same value of

x

, then

HARD

Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 39

Let

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

and

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

, then

HARD

Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 40

Let

f (x) = \frac{40}{3 x^{4} + 8 x^{3} - 18 x^{2} + 60}

. Which of the following statement(s) about

f (x)

is (are) correct ?

HARD

Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 41

Let

f : R \to (0, \infty)

and

g : R \to R

be twice differentiable functions such that

f^{"}

and

g^{"}

are continuous functions on

R

. Suppose

f^{'} (2) = g (2) = 0, f^{"} (2) \neq 0

and

g^{'} (2) \neq 0

, If

\lim_{x \to 2} \frac{f (x) g (x)}{f^{'} (x) g^{'} (x)} = 1

, then

HARD

Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 42

The function

\frac{\sin (x + a)}{\sin (x + b)}

has no maxima or minima, if

HARD

Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 48

The number of the tangents that can be drawn to the curve

y^{2} - 2 x^{3} - 4 y + 8 = 0

from the point

(1, 2)

, is

HARD

Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 21 - Application of Derivatives>Exercise 1>Q 49

If the area enclosed by normal to the curve

y = (1 + x)^{y} + \sin^{- 1} (\sin^{2} x)

at

x = 0

with coordinate axes (in sq. units) is

k

, then the value of

2 k

is