The correct option is D (−∞,−43)∪(2,∞)
∵f′(x)=(4a−3)(1)+(a−7)cos x
=(4a−3(a−7)+cos x)(a−7)
f′(x)≠0
(for non existence of critical points)
4a−3a−7>1 or 4a−3a−7<−1 (∵−1≤cosx≤1)
⇒3a+4a−7>0 or5a−10a−7<0
∴aϵ(−∞,−43)∪(7,∞) or aϵ(2,7)
Hence,aϵ(−∞,−43)∪(2,∞) (∵ at a=7,f′(x)≠0)