How do you find the maximum, minimum and inflection points and concavity for the function #f(x)=6x^6+12x+6#?
Relative minimum at
Always concave up and no inflection points.
To find relative maxima, set
Now, use the sign test to determine the relative maximum and minimum of the function.
For - infinity
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.