Find the maximum and minimum values, if any, of the following functions given by

Question

Find the maximum and minimum values, if any, of the following functions given by f (x) = 9x 2 + 12x + 2

Philoid · Accepted Answer

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.