What's the practical domain and range of this volume function: 4x^3-39x^2+93.5x
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.
To find the practical domain and range of a volume function, we need to look at the possible values of the independent variable (x) and the resulting values of the dependent variable (volume).
1. Practical domain:
The practical domain represents the possible values of x for which the volume function is defined. In this case, since there are no restrictions on the cubic function, the domain is considered to be all real numbers (-∞, +∞). Therefore, the practical domain for the given volume function is (-∞, +∞).
2. Practical range:
To determine the practical range, we need to find the minimum or maximum value that the volume function can take. However, since this is a cubic function, which does not have a direct minimum or maximum value, the practical range for this volume function is (-∞, +∞) as well.
Therefore, both the practical domain and range for the given volume function, 4x^3-39x^2+93.5x, are (-∞, +∞).