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Grade: 11

                        

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

6 years ago

Answers : (2)

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
rajusharma
12 Points
							f(x)= x/sinx
df/dx = (sinx - xcosx)/ (sinx)^2=0
tanx=x
this is only possible when x=0 
it means there is no critical points in the region (0,p/2). so we conclude that the graph of the function is monotonic in nature
						
6 years ago
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