Question

f(x) = 6 + 3x - x3 intervals of increase and decrease. local max and mins. f concave up and concave down. inflection points of f

Answer 1

1) derive to find the critical numbers
2) susbtitute them in the original function to get the local min & max
3) draw a table putting x, f(x) and f'(x) on one side and the x's on a row. Test them from the left of 0, and from the right of 0, ( don't forget to put your critical numbers) then if your sign is (-) then f'(x) is decreasing, if it's (+) f'(x) is increasing
4)derive once more to find the inflection numbers
5) draw a table (same thing with the critical numbers) but this time if it's - , it's concaved down and if it's + it's concaved up

Follow these steps and you'll be alright ^_^ because it'll take more than just 10 mins to solve such question. Good luck!

Hope you understand the steps :)