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inches, express the length of the box in terms of x and then express the volume, V , of
the box in terms of x.
(b) Find the dimensions of the box of maximum volume that can be shipped via Parcel Post.
(c) Repeat parts 3a and 3b if the box is shipped using “other services”. x
length x 17 See here for details. 3.1 Graphs of Polynomials 191 4. Use transformations to sketch the graphs of the following polynomials.
(a) f (x) = (x + 2)3 + 1 (c) h(x) = −x5 − 3 (b) g (x) = (x + 2)4 + 1 (d) j (x) = 2 − 3(x − 1)4 5. Use the Intermediate Value Theorem to ﬁnd intervals of length 1 which contain the real zeros
of f (x) = x3 − 9x + 5.
6. The original function used to model the cost of producing x PortaBoys Game Systems given in
Example 2.1.5 was C (x) = 80x +150. While developing their newest game, Sasquatch Attack!,
the makers of the PortaBoy revised their cost function using a cubic polynomial. The new
cost of producing x PortaBoys is given by C (x) = .03x3 − 4.5x2 + 225x + 250. Market
research indicates that the demand function p(x) = −1.5x + 250 rem...
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