Raghav
Last Activity: 5 Years ago
Question 6. Differentiating, f’(x) = 2cos 2x – 8(a+1)sin x + (4a^2 + 8a – 14)x
=> 2(2 cos^2 x – 1) – 8(a+1)sin x + (..)x
=> 4 ((cos^2 x – 2(a+1)cosx + a^2) + 2a – 4 – 2 cosx)
=> 4((cosx – a)^2 + 2(a – 2 – cosx))
Put f’(x) > 0 bcz we have to find that values for which f is always increasing and has no critical points
=> (cosx – a)^2 + 2(a – 2 – cosx) > 0
(cosx – a)^2 is always greater than (or may be equal to zero)
=> a > 2 + cosx
Max. val. of cosx is 1
So, a € (3, infinity).
It was hard to read this question and solve it like this. Ask the rest separately properly.
