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

2 Answers
May 22, 2018

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

May 22, 2018

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#