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.

Question

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.

Answer 1

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.

Answer 2

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.

Answer 3

(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.