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For Questions 1 and 2, let \(f(x) = x e^{-x}\)

1. Find the largest open interval over which \(f\) is decreasing.

a.  \((-\infty, 0)\)

b.  \((0, \infty)\)

c.  \((1, \infty)\)

d.  \((2, \infty)\)

e.  \((3, \infty)\)

2. Find the largest open interval over which \(f\) is concave up.

a.  \((-\infty, 0)\)

b.  \((0, \infty)\)

c.  \((1, \infty)\)

d.  \((2, \infty)\)

e.  \((3, \infty)\)

3. A cylindrical package to be sent by USPS can have a maximum combined length and circumference of 108 inches (that is, length+circumference\( \leq \) 108 inches). Find the length of the package of maximum volume that can be sent. The formula for the volume of a cylinder is as follows: volume = \(\pi\)(radius)² (length)

a.  24 in

b.  30 in

c.  36 in

d.  48 in

d.  72 in