𝑓(𝑥)=−2𝑥3+42𝑥2−270𝑥+6
For this function there are three important intervals: (−∞,𝐴) and (𝐵,∞) where 𝐴 and B are the critical numbers.
Find
𝐴:
B:
For each of the following intervals, tell whether 𝑓(𝑥) is increasing (type in INC) or decreasing (type in DEC).
(−∞,𝐴):
(𝐴,𝐵):
(𝐵,∞):
𝑓(𝑥) has an inflection point at 𝑥=𝐶
where 𝐶 is:
Finally for each of the following intervals, tell whether 𝑓(𝑥) is concave up (type in CU) or concave down (type in CD).
(−∞,𝐶):
(𝐶,∞):
f increasing where f' > 0
f decreasing where f' < 0
possible inflection point where f" = 0
what do you get?