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JEE Exam  >  JEE Tests  >  Mathematics (Maths) Class 12  >  Test: Increasing And Decreasing Functions - JEE MCQ

Test: Increasing And Decreasing Functions - JEE MCQ


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5 Questions MCQ Test Mathematics (Maths) Class 12 - Test: Increasing And Decreasing Functions

Test: Increasing And Decreasing Functions for JEE 2024 is part of Mathematics (Maths) Class 12 preparation. The Test: Increasing And Decreasing Functions questions and answers have been prepared according to the JEE exam syllabus.The Test: Increasing And Decreasing Functions MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Increasing And Decreasing Functions below.
Solutions of Test: Increasing And Decreasing Functions questions in English are available as part of our Mathematics (Maths) Class 12 for JEE & Test: Increasing And Decreasing Functions solutions in Hindi for Mathematics (Maths) Class 12 course. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free. Attempt Test: Increasing And Decreasing Functions | 5 questions in 10 minutes | Mock test for JEE preparation | Free important questions MCQ to study Mathematics (Maths) Class 12 for JEE Exam | Download free PDF with solutions
Test: Increasing And Decreasing Functions - Question 1
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Separate the interval  into sub-intervals in which f (x) = sin4 x + cos4 x is increasing or decreasing

Detailed Solution for Test: Increasing And Decreasing Functions - Question 1

f’(x) = 4sin3x cosx - 4cos3x sinx
= - sin4x
As x is in the interval [0, ∏/2] hence 4x is in the interval [0, 2∏]

Test: Increasing And Decreasing Functions - Question 2
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The function f(x) = ax, 0 < a < 1 is​

Detailed Solution for Test: Increasing And Decreasing Functions - Question 2

 f(x) = ax
Taking log bth the sides, log f(x) = xloga
f’(x)/ax = loga
f’(x) = ax loga   {ax > 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.

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Test: Increasing And Decreasing Functions - Question 3
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The function  increases in​

Detailed Solution for Test: Increasing And Decreasing Functions - Question 3

 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,∞)

Test: Increasing And Decreasing Functions - Question 4
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The function f (x) = -3x + 12 on R.is​
Detailed Solution for Test: Increasing And Decreasing Functions - Question 4

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

Test: Increasing And Decreasing Functions - Question 5
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What is the nature of function f(x) = x3 – 3x2 + 4x on R?
Detailed Solution for Test: Increasing And Decreasing Functions - Question 5

  f(x) = x3 – 3x2 + 4x

f’(x) = 3x2 – 6x + 4.

f’(x) = 3(x2 – 2x + 1) + 1.

=> 3(x-1)2 + 1>0, in every interval of R. Therefore the function f is increasing on R. 

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