Daily Graph 05-08-09

sin²x(1+sin²x)=y

Dom=R
Range::

-1≤sinx≤1 => 0≤sin²x≤1 & 1≤1+sin²x≤2
=> 0≤sin²x(1+sin²x)≤2

f(x)=f(-x)
=> even function

period=2Ï€/2=Ï€

f(x)=sin ²x + sin⁴x
f'(x)=2sinx.cosx+4sin³xcosx=2sinx.cosx(1+2sin²x)

f'(x)>0 when sinx.cosx>0 =>x ε[0,π/2]
f'(x)<0 when sinx.cosx<0 =>x ε[π/2,π]
f'(x)=0 => sinx=0 or cosx=0
=> x=nπ or x=(2m+1)π/2
=> x=0,Ï€... or x=Ï€/2,3Ï€/2...

easy now..