find the intervals in which the function f(x)=tan x -4x where x belongs to (0, pie/2) is strictly increasing b) strictly decreasing
Answers
Given : f(x)= tan x -4x where x belongs to (0, π/2)
To Find : intervals in which the function is strictly increasing b) strictly decreasing
Solution:
f(x)=tan x -4x
f'(x) = sec²x - 4
for strictly increasing interval f'(x) > 0 => sec²x - 4 > 0
=> sec²x > 4
=> Secx > 2 Secx is + ve in ( 0 , π/2)
Hence π/3 < x < π/2
for strictly decreasing interval f'(x) < 0 => sec²x - 4 < 0
=> sec²x < 4
=> 0 < Secx < 2 as secx is + ve in ( 0 , π/2)
Hence strictly decreasing for 0 < x < π/3
strictly decreasing for 0 < x < π/3
strictly increasing for π/3 < x < π/2
Learn More:
Find the interval in which f(x)=cos 3x iw strictly increasing or ...
https://brainly.in/question/8903430
A positive integer n is called strictly ascending if it's digits are in the ...
https://brainly.in/question/14118235