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f(X)= x÷sinx in (0,p÷2) check the monotonicity?

VENU , 11 Years ago
Grade Upto college level
anser 1 Answers
bharat bajaj

Last Activity: 11 Years ago

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.
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