Find the maximum and minimum values, if any, of the following functions given by
f (x) = 9x2 + 12x + 2
It is given that f (x) = 9x2 + 12x + 2 = (3x + 2)2 - 2
Now, we can see that (3x + 2)2 ≥ 0 for every x ϵ R
⇒ f (x) = (3x + 2)2 - 2 ≥ -2 for every x ϵ R
The minimum value of f is attained when 3x + 2 = 0
3x +2 =0
Then, Minimum value of 
Therefore, function f does not have a maximum value.
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