Page 298 - Calculus Demystified

Chapter 3
y 285

x

Fig. S3.13

while the cost of the sides is
C 2 = 4(s · h) · 20 cents.
We find that the total cost is
2
C = C 1 + C 2 = 20s + 80sh. (∗)
But
2
100 = volume = s · h
hence
2
h = 100/s .
Substituting this last formula into (∗) gives
8000
2 2 2
C(s) = 20s + 80s ·[100/s ]= 20s + .
s
We may calculate that
8000

0 = C (s) = 40s − .
s 2
Solving for s gives the solution s ≈ 5.8479 and then h ≈ 2.9241.
15. We see that
2
x − 1
f(x) =
2
x + 1
4x

f (x) =
2
(x + 1) 2
2
−12x + 4

f (x) =
2
(x + 1) 3