Description

This mock test of Test: Increasing And Decreasing Functions for JEE helps you for every JEE entrance exam.
This contains 5 Multiple Choice Questions for JEE Test: Increasing And Decreasing Functions (mcq) to study with solutions a complete question bank.
The solved questions answers in this Test: Increasing And Decreasing Functions quiz give you a good mix of easy questions and tough questions. JEE
students definitely take this Test: Increasing And Decreasing Functions exercise for a better result in the exam. You can find other Test: Increasing And Decreasing Functions extra questions,
long questions & short questions for JEE on EduRev as well by searching above.

QUESTION: 1

Separate the interval into sub-intervals in which f (x) = sin4 x + cos4 x is increasing or decreasing

Solution:

f’(x) = 4sin^{3}x cosx - 4cos^{3}x sinx

= - sin4x

As x is in the interval [0, ∏/2] hence 4x is in the interval [0, 2∏]

QUESTION: 2

The function f(x) = a^{x}, 0 < a < 1 is

Solution:

f(x) = a^{x}

Taking log bth the sides, log f(x) = xloga

f’(x)/a^{x} = loga

f’(x) = a^{x} loga {a^{x} > 0 for all x implies R,

for loga e<a<1 that implies loga < 0}

Therefore, f’(x) < 0, for all x implies R

f(x) is a decreasing function.

QUESTION: 3

The function increases in

Solution:

f'(x) = [(logx).2−2x.1/x](logx)^{2}

= 2(logx−1)/(logx)^2

∴f'(x)>0

⇔logx−1>0

⇔logx>1

⇔logx>loge

⇔x>e

∴f(x) is increasing in (e,∞)

QUESTION: 4

The function f (x) = -3x + 12 on R.is

Solution:

f(x) = -3x + 12

f(0) = -3(0) + 12 = 0 - 12 = 0

f(1) = 9

f(2)= 6

f(3) = 3

f(4) = 0

f(5) = -3

QUESTION: 5

The function is

Solution:

f(x) = x + 1/x

f’(x) = 1 - 1/x^{2}

= (x^{2} - 1)/x^{2}

= [(x - 1) (x + 1)]/x^{2}

= x ≥ 1

Therfore, x - 1 ≥ 0, x + 1 ≥ 0

[(x - 1) (x + 1)]/x^{2} ≥ 0

f’(x) ≥ 0 => f(x) is increasing.

### Increasing and Decreasing Functions

Video | 07:32 min

### Increasing and Decreasing Functions at a Point

Video | 05:32 min

### INCREASING & DECREASING FUNCTION

Doc | 9 Pages

- Test: Increasing And Decreasing Functions
Test | 5 questions | 10 min

- Test: Functions
Test | 20 questions | 35 min

- Test: Functions
Test | 15 questions | 15 min

- Test: Functions- 3
Test | 15 questions | 30 min

- Test: Logarithmic Functions
Test | 10 questions | 10 min