1f|(x)=4sin3x cosx -4cos3x sinx
=4sinxcosx(sin2x=cos2x)
=-2sin2x(cos2x)
=-sin4x
-sin4x>0 (as f|(x) is increasing)
sin4x<0
pi<4x<2(pi)
pi/4<x<pi/2
only option (b) lies in the range therefore (b) is the ans
The function f(x)=sin4x+cos4x increases if
(a)0<x<pi/8
(b)pi/4<x<3pi/8
(c)3pi/8<x<5pi/8
(d)5pi/8<X<3pi/4
-
UP 0 DOWN 0 0 2
2 Answers
1first the options look horrible and u can't check by putting values,,,,,,,so put t=2x
now it looks as
f(x)=sin4 t/2 + cos4 t/2
ofcourse the options simplify too...
now as usual diffrentiateand ultimately u should get
f|(t)=sin t (2sin2t/2 - 1)
Now all we hav to find is where f|(t) is positive and then put t=2x.....i think the prob is now solved
1