Question

已知f(x)=sin2x-x,则在区间【-2分之派,2分之派】上的最大值为?最小值为?

Answer 1

f'(x)=2cos2x-1令f'(x)>0,得cos2x>1/2,即2x∈[-π/3+2kπ,π/3+2kπ],即x∈[-π/6+kπ,π/6+kπ]又∵x∈[-π/2,π/2],∴x∈[-π/6,π/6]令f'(x)=0,得x=±π/6令f'(x)-π/2,所以最小值为端点值f(π/2)=-π/2∵极大值...