Given the function [tex] f(x)=3x^2-18x+23 [/tex]. The above function can be written as
[tex] f(x)=3x^2-18x+23\\
f(x)=3(x^2-6x)+23\\
f(x)=3(x^2-6x+9-9)+23\\
f(x)=3(x-3)^2-27+23\\
f(x)=3(x-3)^2-4 [/tex]
a)Now, the function [tex] f(x)=3(x-3)^2-4 [/tex] has minimum value since the coefficient of [tex] (x-3)^2 [/tex] is [tex] 3>0 [/tex].
b) The minimum value of the function occurs at [tex] x=3 [/tex] and its value is
[tex] f(3)=3(3-3)^2-4 =-4 [/tex]
c)The minimum value of the function occurs at [tex] x=3 [/tex].
