Asked by Allie
What's the practical domain and range of this volume function: 4x^3-39x^2+93.5x
Answers
Answered by
Damon
for large |x| the function is dominated by x^3
so
for a large value of x the function is large positive
for a large negative x the function is large negative
so
the range is -oo to +oo
HOWEVER if it describes a volume, it must be +
where is it + ?
find the zeros
v = x (4x^2 -39 x + 93.5)
0 at x = 0 of course
also at x = [ 39 +/- 5 ] / 8
or x = 5.5 and 4.25
so the function comes up from -oo to x = 0, then is positive from x = 0 to x = 4.25, then is negative from x = 4.25 to x = 5.5. Then it heads off to the upper right. Hope that helps.
so
for a large value of x the function is large positive
for a large negative x the function is large negative
so
the range is -oo to +oo
HOWEVER if it describes a volume, it must be +
where is it + ?
find the zeros
v = x (4x^2 -39 x + 93.5)
0 at x = 0 of course
also at x = [ 39 +/- 5 ] / 8
or x = 5.5 and 4.25
so the function comes up from -oo to x = 0, then is positive from x = 0 to x = 4.25, then is negative from x = 4.25 to x = 5.5. Then it heads off to the upper right. Hope that helps.
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