Question

已知函数f(x)=2asinx*cosx+2bcos^2x,且f(0)=8,f(pai/6)=12.

Answer 1

y=2*a*sin(x)*cos(x)+2*b*cos(x)^2

f(0)=2*b=8

b=4

f(pi/6)=sqrt(3)a/2+1.5b=12

a=4sqrt(3)

解f'(x)=0得x=-pi/3,x=pi/6

检验得y=-4,y=12

取x=pi/6,y=12