Question

The maximum value of the function f(x)=(3cosx-2)^2-2 ?

Answer 1

Maximum value = 23

Explanation:

`f(x)=[3cos(x)-2]^2-2`

`f'(x)=2sin(x)[3cos(x)-2] * [-3sin(x)]`
`f'(x)= -6sin(x)[3cos(x)-2]=0`
`sin(x)[3cos(x)-2]=0`

`sin(x)=0`
`x=2kpi+-pi`
`x=pi`
#f(pi)=[-3-2]^2-2=25-2=23

`3cos(x)-2=0`
`cos(x)=2/3`
`x=2kpi+-cos^-1(2/3)`
`f(2kpi+-cos^-1(2/3))=-2`

Obviously the minimum value of the function is -2 and the maximum value of the function is 23

Answer 2

f(x)max = -1

Explanation:

The unique variable here is cos x that reaches max when cos x = 1
The maximum value is:
`f(x) = (3 - 2)^2 - 2 = 1 - 2 = - 1`