Suppose that f(x), f'(x), and f''(x) are continuous for all real numbers x, and the f has the following properties. I. f is negative on (-inf, 6) and positive on (6,inf). II. f is increasing on (-inf, 8) and positive on 8, inf).
Find the open intervals on which f(x) = -6x^2 + 96x + 7 is increasing or decreasing. a. increasing on (-inf, 16); decreasing on (16, inf). b. increasing on (-inf, 14); decreasing on (14, inf). c. increasing on (-inf, 84);
Find the intervals on which x^2/(x-3)^2 is decreasing. a. (0,6) b. (0,3), (3,6) c. (-inf,0), (6,inf) The critical numbers are x=0 and 6, but since there is an asymptote at x=3, I'm not sure whether a or b is the answer.
6. f(x)= 12x^5 + 30x^4 - 160x^3 +4 For this function there are four important intervals:(-inf, A] , [A,B] ,[B,C],[C, inf) where A ,B ,C are the critical numbers. Find A B AND C and at those points do they have a local min, max or
Let A=(-2,INF] and B=(2,INF). FIND: a.)AUB b.)A (UPSIDE DOWN "U")B c.)A\B d)B\A *I was thinking a was (-2,inf), b was (-1,2), c was (-1,1) and d was (2,inf) but i don't think that is right since i don't have a U in the answers.
Consider the function f(x)=-2x^3+33x^2-108x+2. For this function, there are three important intervals: (-Inf,A], [A,B], [B,Inf) where A and B are the critical points. Find A and B and for each of the important intervals, tell