posted by jeff .
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.
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.
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.
(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.