Find the intervals on which the function is concave up or down, the points of inflection, and the critical points, and determine whether each critical point corresponds to a local minimum or maximum (or neither). Let $$f(x) = -\left(3x+3\sin\!\left(x\right)\right), \; 0 \le x \le 2 \pi$$

What are the critical point(s) =
What does the Second Derivative Test tell about the first critical point: ? Local Max Local Min Test Fails ?
What does the Second Derivative Test tell about the second critical point: ? Local Max Local Min Test Fails Only one critical point on interval ?

What are the inflection Point(s) =

On the interval to the left of the critical point, $f$ is ? Increasing Decreasing and $f'$ is ? Positive Negative . (Include all points where $f'$ has this sign in the interval.)
On the interval to the right of the critical point, $f$ is ? Increasing Decreasing and $f'$ is ? Positive Negative . (Include all points where $f'$ has this sign in the interval.)

On the interval to the left of the inflection point $f$ is ? Concave Down Concave Up . (Include only points where $f$ has this concavity in the interval.)
On the interval to the right of the inflection point $f$ is ? Concave Down Concave Up . (Include only points where $f$ has this concavity in the interval.)