Homework SourseFor the function fx2x354x14 find all intervals where the fun
For the function f(x)=2x^3-54x+14, find all intervals where the function is increasing:
f is increasing on _________?
(Give your answer as an interval or a list of intervals, e.g., (-infinity,8] or (1,5),(7,10) .)
Similarly, find all intervals where the function is decreasing:
f is decreasing on ________?
(Give your answer as an interval or a list of intervals, e.g., (-infinity,8] or (1,5),(7,10) .)
Finally, find all critical points in the graph of f(x)
critical points: x=
f is increasing on _________?
(Give your answer as an interval or a list of intervals, e.g., (-infinity,8] or (1,5),(7,10) .)
Similarly, find all intervals where the function is decreasing:
f is decreasing on ________?
(Give your answer as an interval or a list of intervals, e.g., (-infinity,8] or (1,5),(7,10) .)
Finally, find all critical points in the graph of f(x)
critical points: x=
Solution
df/dx>0 6x^2-54>0 x^2-9>0 x>3 or x<-3 (-infinity,-3],[3,infinity) df/dx<0 -3
