(1)把f(x)變形為
f(x)=2t2-6t+3-(sinx+t)^2
當(dāng)t>1時(shí),f(x)的最小值g(t)=2t2-6t+3-(-1+t)^2=t2-4t+2
當(dāng)t<1時(shí),f(x)的最小值g(t)=2t2-6t+3-(1+t)^2=t2-8t+2
當(dāng)-1≤t≤1時(shí),f(x)的最小值g(t)=2t2-6t+3
(2)
-1≤t≤1時(shí),g(t)=2t2-6t+3
2t2-6t+3=kt
k=2t+3/t-6
當(dāng)-1≤t≤0
-2t-3/t≥2√6
2t+3/t-6≤-2√6-6
k≤-2√6-6
當(dāng)0≤t≤1
2t+3/t≥2√6
2t+3/t-6≥2√6-6
k≥2√6-6
所以k≤-2√6-6或k≥2√6-6