21pl. tell r da obsevatn in post 5 correct???
so i know if i can proceed like dat or not
Let f'(sinx)<0 and f"(sinx)>0, for all x belonging to (0,pi/2) and g(x)=f(sinx)+f(cosx) then..
a) g(x) is increasing in x ε (0,pi/4)
b) g(x) is increasing in x ε (pi/4,pi/2)
c) g(x) decreases in (0,pi/4)
d) g(x) is increasing in x ε (0,pi/2)
(More than one correct..)
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35 Answers
21
1g'(x) = cosx f'(sinx) - sinxf'(cosx)
for 0 to pi/4,
cosx>0, f'(sinx)<0
so cosx f'(sinx) <0 say its -A.
case1: f'(cosx) >0
and sinx>0 onlly.
so, sinxf(cosx) >0
so whole g(x)<0 => decreasing.
case2: f'(cosx)<0
but sinx>0
so sinxf(cosx) <0 .... say -B
so g(x)= -A +B
now, for 0 to pi/4, cosx>sinx
so, -A+B <0
so g(x) is decreasing for 0 to pi/4.
1well one assumption in the last step... f'(cosx) is less negative than f'(sinx) .
