Answer:
[tex]f(x)=-13[/tex]
Step-by-step explanation:
[tex]f(x)=3x^2 + 18x + 14[/tex]
[tex]f^{'}(x)=6x + 18[/tex]
But to find the minimum value, we would have to find the value of x at which [tex]f(x)[/tex] is at minimum. To do this [tex]f^{'}(x)=0[/tex].
[tex]6x+18=0[/tex]
[tex]x=-3[/tex]
Substituting the minimum value of x into [tex]f(x)[/tex]
[tex]f(x)=3(-3)^2 + 18(-3) + 14[/tex]
[tex]f(x)=-13[/tex]
[tex]\therefore[/tex] the minimum value of [tex]f(x)=-13[/tex]
