#### Question

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

*f*(*x*) = 9*x*^{2} + 12*x* + 2

#### Solution

The given function is *f*(*x*) = 9*x*^{2} + 12*x* + 2 = (3*x* + 2)^{2} − 2.

It can be observed that (3*x* + 2)^{2} ≥ 0 for every *x* ∈ **R**.

Therefore,* f*(*x*) = (3*x* + 2)^{2} − 2 ≥ −2 for every *x* ∈ **R**.

The minimum value of *f* is attained when 3*x* + 2 = 0.

Hence, function *f* does not have a maximum value.

Is there an error in this question or solution?

Solution Find the Maximum and Minimum Values, If Any, of the Following Functions Given by F(X) = 9x2 + 12x + 2 Concept: Maxima and Minima.