Find the max or min value for y given the restictions on x.
y= x^3 -x^2 -6x
a) 0<x<3 min
b) -2<x<0 max
4 answers
what is tttt?
y = x^3 - x^2 - 6x = 0(x+2)(x-3)
y' = 3x^2 - 2x - 6
y' = 0 at approximately 1.7, -1.1 (1 +- sqrt(19))/3.
Knowing what we do about the shape of cubics, we can say that a local max is at x=-1.1, and a local min is at x=1.7
Note how the given intervals correspond to exactly one "hump" of the graph, so the local min/max is the min/max for that interval.
y' = 3x^2 - 2x - 6
y' = 0 at approximately 1.7, -1.1 (1 +- sqrt(19))/3.
Knowing what we do about the shape of cubics, we can say that a local max is at x=-1.1, and a local min is at x=1.7
Note how the given intervals correspond to exactly one "hump" of the graph, so the local min/max is the min/max for that interval.
I don't understand the y' stuff. I'm only in algebra. Is there another way?
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