y=x^3-3x. Fill out the following table and then make a rough sketch of the graph.
I can make the sketch just having trouble understanding what is wanted.
y=0 when
y'=0 when
Relative Max(s)
Relative Min(s)
y'>0 on the interval(s)
y'<0 on the interval(s)
y is increasing on the interval(s)
y is decreasing on the interval(s)
so i got so far
y=0 when x=0
y'=0 when x=1
rel max (-1,2)
rel min (1,-2)
y'>0 on interval(s) ????
y'<0 on interval(s) ????
y is increasing on (-infinity,2)(-2,infinity)
y decreasing on (2,-2)
y'> 0 on the intervals
This means, for what range of x values is y' = 3x^2 - 3 positive, or in other words, for what range of x values is the graph of y' above the x axis
y' < 0
This means for what range of x values is y'= 3x^2 -3 negative, or in other words, for what range of x values is the graph of y' below the x axis