Grade 11Algebra

Check the monotonicity of f (x) = x sin x in (0, p/2).

Amarnath

12 Years agoGrade 11

3 Answers

Parvez ali

12 Years ago

Thanks & Regards

Parvez Ali

askIITians Faculty

Sher Mohammad

Approved Tutor Answer12 Years ago

f'(x)=sinx+xcosx

f'(x)>0 between (0,pi/2)

hence the function is monotonically increasing.

Sher Mohammad

B.Tech, IIT Delhi

bharat bajaj

12 Years ago

f(x)= x/sinxdf/dx = (sinx - xcosx)/ (sinx)^2

A function is monotonic if it is either increasing or decreasing in the given range.
Hence, check the sign of df/dx.

df/dx = (tanx - x)cosx/(sinx)^2

tan x - x> 0 for (0,pi/2) . You may check it by making the graph.
cosx>0 for (0,pi2)
Hence, df/dx>0 for(0,pi/2)
Hence, this function is monotonic in the given range.
Thanks & Regards
Bharat Bajaj
askIITians Faculty
IIT Delhi