求f(x)的最大值、最小值,及他们的图像（说出方法即可,画出清晰图且正确者加分）f(x)=cosx+sinxf(x)=cosx-sinxf(x)=5cosx+12sinxf(x)=4cos5x+5sin5x

Question

求f(x)的最大值、最小值,及他们的图像（说出方法即可,画出清晰图且正确者加分）
f(x) = cosx + sinx
f(x) = cosx - sinx
f(x) = 5cosx + 12sinx
f(x) = 4cos5x + 5sin5x

Answer 1

f(x)=cosx+sinx
f(x)^2=(cosx+sinx)^2=cosx^2+sinx^2+2cosxsinx=1+2cosxsinx=1+sin2x
f(x)^2max=2 f(x)max=√2,f(x)min=-√2
同理
f(x) = cosx - sinx f(x)max=√2,f(x)min=-√2
然而
f(x) = 5cosx + 12sinx
f(x)max=17√2/2,f(x)min=-17√2/2
f(x) = 4cos5x + 5sin5x
f(x)max=9√2/2,f(x)min=-9√2/2