For every pair of continuous functions f , g : 0 , 1 → R such that max f x : x ∈ 0 , 1 = max { g x : x ∈ 0 , 1 } , then the correct statement(s) is(are)

f c 2 = g c 2 for some c ∈ 0 , 1

f c 2 + f c = g c 2 + 3 g c for some c ∈ 0 , 1

f c 2 + 3 f c = g c 2 + g c for some c ∈ 0 , 1

For every pair of continuous functions f , g : 0 , 1 → R such that max f x : x ∈ 0 , 1 = max { g x : x ∈ 0 , 1 } , then the correct statement(s) is(are)

f c 2 = g c 2 for some c ∈ 0 , 1

Let f : R → R be defined by f x = x 2 - 3 x - 6 x 2 + 2 x + 4 Then which of the following statements is(are) TRUE?

f is increasing in the interval ( 1 , 2 )

Let f : R → R be given by f x = x - 1 x - 2 x - 5 . Define F x = ∫ 0 x f t d t , x > 0 . Then which of the following options is/are correct?

F has two local maxima and one local minimum in 0 , ∞

Let T denote a curve y = y x which is in the first quadrant and let the point 1 , 0 lie on it. Let the tangent to T at a point P intersect the y -axis at Y P . If P Y P has length 1 for each point P on T , then which of the following options is/are correct?

y = - l o g e 1 + 1 - x 2 x + 1 - x 2

If f : R → R is a differentiable function such that f ′ x > 2 f ( x ) for all x ∈ R and f 0 = 1 then

f x i s i n c r e a s i n g i n ( 0 , ∞ )

f x i s d e c r e a s i n g i n ( 0 , ∞ )

f ' ( x ) < e 2 x in ( 0 , ∞ )

E M B I B E

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>JEE Advanced Paper 1 - 2014>Q 17

HARD

JEE Advanced

IMPORTANT

Earn 100

For every pair of continuous functions $f, g : [0, 1] \to R$ such that $\max \{f (x) : x \in [0, 1]\}$ $= \max {g (x) : x \in [0, 1]}$ , then the correct statement(s) is(are)

100% studentsanswered this correctly

Important Questions on Application of Derivatives

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>JEE Advanced Paper 1 - 2013>Q 19

The number of points in

(- \infty, \infty)

, for which

x^{2} - x \sin x - \cos x = 0

, is:

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Application of Derivatives>JEE Advanced Paper 1 - 2013>Q 20

A rectangular sheet of fixed perimeter with sides having their lengths in the ratio $8 : 15$ is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is $100$ , the resulting box has maximum volume. Then the lengths of the sides of the rectangular sheet are: