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Grade: 11
        Check the monotonicity of f (x) =
x
sin x
in (0, p/2).
6 years ago

Answers : (3)

Parvez ali
askIITians Faculty
47 Points
							
147-607_140303-103201.jpg



Thanks & Regards
Parvez Ali
askIITians Faculty

6 years ago
Sher Mohammad
IIT Delhi
askIITians Faculty
174 Points
							f'(x)=sinx+xcosx

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

hence the function is monotonically increasing.

Sher Mohammad
B.Tech, IIT Delhi


6 years ago
bharat bajaj
IIT Delhi
askIITians Faculty
122 Points
							
f(x)= x/sinx
df/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
6 years ago
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