Posted by **jeff** on Tuesday, July 8, 2008 at 4:24pm.

At noon, ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 4:00 pm.

Find the intervals of increase or decrease

find the local maxiumum and minimum values

find the intervals of concavity and the inflection points.

b(x) = 3x^2/3 - x

a rectangular storage container with an open top is to have a volume of 10 m^3. the length of its base is twice the width. Material for the base costs $10 per square meter. Material for the sides cost $6 per square meter. Find the cost of the materials for the cheapest such container.

- math (calc) -
**drwls**, Tuesday, July 8, 2008 at 5:02pm
There are three totally different questions posted here. I will be happy to respond to any of them in which work is shown by you.

- math (calc) -
**Reiny**, Tuesday, July 8, 2008 at 6:33pm
As drwls indicated, we are not here to merely do the work for you.

You have posted 3 routine calculus questions.

I will get you going on the first one which deals with "rates of change"

After t hours, distance traveled by ship A is 35t km and that of ship B is 25t km

Did you make a diagram?

If you let the distance between them be y km, then

y^2 = (150-35t)^2 + (25t)^2

find dy/dt and sub in t=4 (4:00 pm)

Let me know what answer you got.

- math (calc) (#2 of 3) -
**drwls**, Tuesday, July 8, 2008 at 7:04pm
(2) Intervals of increase are where db/dx > 0

Intervals of decrease are where db/dx < 0

db/dx = 2x - 1

d^2b/dx^2 = 2

Inflection points are where d^b/dx^2 = 0. There appear to be no such points.

Intervals of concavity (upward) occurwhere d^b/dx^2 > 0

Maximum and minimum values occur where db/dx = 0. Use the second derivative test to determime if it is a maximum or a minimum.

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