|
f(x)=a(sinx-cosx)-2sinxcosx∵(sinx-cosx)^2=1-2sinxcosx∴2sinxcosx=1-(sinx-cosx)^2设 t=sinx-cosx=√2sin(x-π/4)∈[-√2,√2]∴2sinxcosx=1-t^2f(x)=at+t^2-1=(t+a/2)^2-a^2/4-1当-a/2∈(-√2,√2),即-2√2<a＜2√2时t=-a/2,f(x)min=-a^2/4-1当-a/2≥√2即a≤-2√2时 t=√2,f(x)min=√2a+1当-a/2≤-√2即a≥2√2时, t=-√2,f(x)min=-√2a+1... |
