Given the function $g(z) = 6z^3 - 45z^2 + 108z$, find the first derivative, $g'(z)$.
$g'(z) =
$
Notice that $g'(x) = 0$ when $z = 3$, that is, $g'(3) = 0$.
Now, we want to know whether there is a local minimum or local maximum at $z = 3$, so we will use the
second derivative test.
Find the second derivative, $g''(z)$.
$g''(z) =
$
Evaluate $g''(3)$.
$g''(3) =
$
Based on the sign of this number, does this mean the graph of $g(z)$ is concave up or concave down at
$z = 3$?
At $z = 3$ the graph of $g(z)$ is Select an answer
Based on the concavity of $g(z)$ at $z = 3$, does this mean that there is a local minimum or local maximum
at $z = 3$?
At $z = 3$ there is a local Select an answer
