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Check the monotonicity of f(x)=x÷sinx in (0,p÷2)

Check the monotonicity of f(x)=x÷sinx in (0,p÷2)

Grade:12

2 Answers

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
7 years ago
f'(x)=sinx+xcosx/(sinx)^2=1/sinx(x)+xcos(x)/(sinx)^2
f'(x)>0 for all x in 0 to p/4
hence function in monotonically increasing.


Sher Mohammad
B.Tech, IIT Delhi
Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
7 years ago
f'(x)=sinx-xcosx/(sinx)^2

for small x, sinx=x
f'(x)=x(1-cos x)> greater than zero
for higher values of x, also f'(x)>0, hence the function f(x) is monotonically increasing.

Sher Mohammad
B.Tech, IIT Delhi

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