Question

Find the minimum value of $f\left(n\right)=3n^2-6n-11$.

Answer 1

$f\left(n\right)=3n^2-6n-11$
f'(n) =6n-6 f(n) is minimum when f(n) =0
$6n-6=0\Rightarrow x=\frac{6}{6}=1$
least value of $f\left(n\right)=f\left(1\right)=3\times 1-6-11$
=3 -17
=-14