Question

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

(ii) f(x) = 9x² + 12x + 2

Answer 1

(ii) The given function is f(x) = 9x² + 12x + 2 = (3x + 2)² −2. 

It can be observed that (3x + 2)2 ≥ 0 for every x ∈ R.
Therefore, f(x) = (3x + 2)² − 2 ≥ −2 for every x ∈ R.
The minimum value of f is attained when 3x + 2 = 0.

Hence, function f does not have a maximum value.