Q1 of 168 Page 231

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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