MMMhhh?
Both I and bobpursley answered you .
http://www.jiskha.com/display.cgi?id=1390567139
Why are you reposting?
Hi, Please help me find: V, a, and b. Ty
An open box is to be made from a flat piece of material 8 inches long and 2 inches wide by cutting equal squares of length x from the corners and folding up the sides.
Write the volume V of the box as a function of x. Leave it as a product of factors, do not multiply out the factors.
V= ?
If we write the domain of the volume of the box as an open interval in the form (a,b), then what is a=?
a= ?
and what is b=?
b=
3 answers
L = 8 - 2x
W = 2 - 2x
V = L W x
V = (8-2x)(2-2x)x
V = 4(4-x)(1-x)x
V = 4 x (4 -5x + x^2)
V/4 = x^3 - 5x^2 + 4x
If x is > 1 that is impossible because the width will be negative
if x is 0, our volume is 0
I wonder where V is maximum?
where is derivative = 0?
f' = 3 x^2 -10 x + 4
that is 0 when
x = [ 10 +/- sqrt(100 - 48)]/6
x = [ 10 +/- 7.21]/6
x = .465 or 2.88
2.88 is outside of our domain or x so
max V when x = .465
so domain of V is from 0 to V(.465)=3.52
W = 2 - 2x
V = L W x
V = (8-2x)(2-2x)x
V = 4(4-x)(1-x)x
V = 4 x (4 -5x + x^2)
V/4 = x^3 - 5x^2 + 4x
If x is > 1 that is impossible because the width will be negative
if x is 0, our volume is 0
I wonder where V is maximum?
where is derivative = 0?
f' = 3 x^2 -10 x + 4
that is 0 when
x = [ 10 +/- sqrt(100 - 48)]/6
x = [ 10 +/- 7.21]/6
x = .465 or 2.88
2.88 is outside of our domain or x so
max V when x = .465
so domain of V is from 0 to V(.465)=3.52
by the way, I would call that the range of V
the domain of x is 0 to 1
the domain of x is 0 to 1