Page 114 - How To Solve Word Problems In Calculus

400
= 4
x 2
2
4x = 400
2
x = 100
x = 10
Since y = 50/x, the corresponding value of y is 5. The dimen-
sions of the poster are x + 8 = 18 in by y + 4 = 9 in.
Step5 (Optional)

A (x) =−400x −2 + 4
A (x) = 800x −3

800
=
x 3
800

A (10) = > 0
1000
A positive second derivative at the critical number tells us we
have a relative minimum. Because there is only one relative
extremum on the interval (0, ∞), A(x) has an absolute mini-
mum at 10.

EXAMPLE 15
At 12:00 noon ship B is 100 miles east of ship A. If ship B
sails west at 10 mi/h and ship A sails south at 20 mi/h, when
will the ships be closest to each other? What is the distance
between them at that time?

Solution
Step1
100
Noon:
A B
x B

y z

A
101