Find where f(x)=4x-\tan x, \ -\pi/2<x<\pi/2 is increasing or decreasing and find it's maximum and minimum values

Dottie Parra 2021-09-15 Answered

Find where f(x)=4xtanx, π2<x<π2 is increasing or decreasing and find it's maximum and minimum values.

You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Nola Robson
Answered 2021-09-16 Author has 94 answers

f(x)=4xtanx, π2<x<π2
differentiating f(x) with respect to x, f(x)=4sec2x
now, ,f(x)=4sec2x=0
4sec2x=0
sec2x=22
secx=±2
x=±π3
so, there are three intervals.(π2,π3),(π3,π3),(π3,π2) let's check f'(x)>0 in which intervals. π3secx<2 so, f(x)=4sec2x>0
hence,f(x)is increasing in(π3,π3)
similarly,check f(x)value(π2,π3)and(π3,π2)
you will get f(x)<0 from this intervals
so,f(x)is decreasing(π2,π3)(π3,π2)
again differentiate with respect to x, f(x)=02sec2x.tanx=2sec2x.tanx
atx=π3,fπ3)=2sec2(π3).tan(π3)<0
hence,f(x)is maximum at x=π3

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

New questions