# How do you find the maximum, minimum and inflection points and concavity for the function #f(x)=6x^6+12x+6#?

##### 1 Answer

Jun 20, 2016

Relative minimum at

Always concave up and no inflection points.

#### Explanation:

To find relative maxima, set

So,

Now, use the sign test to determine the relative maximum and minimum of the function.

For - infinity

For

Therefore, the function has relative minimum at

Regarding concavity of the function, since the second derivative is always positive, we can determine that the function is always concave up and has no inflection points.