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.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.