In this problem you are asked to find a function that models a real-life situati
ID: 2912145 • Letter: I
Question
In this problem you are asked to find a function that models a real-life situation and then use the model to answer questions about the situation. Use the guidelines on page 237 to help you.
A wire 16 cm long is cut into two pieces, one of length x and the other of length 16 x, as shown in the figure. Each piece is bent into the shape of a square.
(a) Find a function that models the total area A enclosed by the two squares in terms of x.
A(x) =
(b) Find the value of x that minimizes the total area of the two squares.
x = cm
Explanation / Answer
a. A(x) = x2+(16-x)2 = x2+ 256-32x+x2 = 2x2-32x +256
A(x)= 2x2-32x +256
b. A'(x) = 4x-32
A"(x) =4>0
A'(x)=0
4x-32=0
x=8
v. x=8cm
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