Calculus
posted by sh .
How fast is the area of a square increasing when thh side is 3m in length and growing at a rate of 0.8m/min?
I did Area=x^2
Area'=2x(x')
x'=area'/2xz
x'=0.8/((2)(3))
Where did I go wrong? Thanks in advance.

Watch the units!!!
The length is growing at 0.8 mm/min. So
dx/dt
=0.8 mm/min.,
=0.0008 m/min, and
x=3 m
The required answer is
d(Area)/dt=2x.dx/dt as you have worked out. 
The given rate is 0.8m/min, so the conversion is not needed. The answer given at the back is 4.8m^2/min, but the answer I have is 0.13.

"x'=area'/2xz
x'=0.8/((2)(3)) "
is not correct.
You have already worked out
Area'=2x(x') which is equivalent to
d(area)/dt = 2x*(dx/dt)
So substitute numerical values to get the right answer! 
Oh, dx/dt=0.8m/min, I thought Area' was, thanks :)

A rectangular box with a square base and top is to be made to contain 1250 cubic feet. The material for the base costs 35 cents per square foot, for the top 15 cents per square foot, and for the sides 20 cents per square foot. Find the dimensions that will minimize the cost of the box.

You would have a better chance to make a new post in case I am absent from my desk. Sometimes piggyback questions don't get the attention that they deserve.
In any case, would you like to show me what you've done? It's a very similar problem as the previous.
You would assume the side of the square (base or top) to be x (feet).
The height can be expressed in terms of x and the volume. (V=L*W*H=x²*H)
You would then express the sum of the costs, C, made up of
1. the cost of the base = area of base * unit cost of base,
2. the cost of the sides and
3. the cost of the top.
Now differentiate C(x) with respect to x and equate C'(x)=0. Solve for x.