for f(x) = - 1/2 x⁴+ 2/3 x³ + 5 determine the

1. 1 st derivative
2. Critical Numbers: where f'(x) is undefined & solution to f'(x) = 0

Critical #s: x =_________________________

1. Intervals of Increase & Decrease and Locations of Max & Min Points based on the 1 st Derivative Test indicating these values on a sign diagram *note: show your work involving test values used
2. 2nd Derivative
3. Location of Inflection Points: solution(s) to f''(x) = 0
4. Intervals of Concavity indicated on a sign diagram *showing the "test values" used