已知:函数f(x)=2asinxcosx+2bcos平方x,f(派/6)=3(根号3)/2+6,f(0)=8
(1)求a\b的值
(2)求f(x)的最大值
參考答案:f(x) = 2a*sinx*cosx + 2b*cosx*cosx
= a*sin(2x) + b(1 + cos2x)
f(0) = 2b = 8 .... b = 4
f(π/6) = a*√3/2 + 4*(1 + 1/2) = 3√3/2 + 6
a = 3
f(x) = 3*sin(2x) + 4*cos(2x) + 4
= 5*sin(2x + A) + 4
A = arctg(4/3)
fmax = 5 + 4 = 9