how to teach

02-26-2012, 05:37 AM

In an open box with quadratic bottom and volume V the side is called c and the hight is called h.

a) Find h expressed by x and V

Easy: V=x^2*h

so h=V/x^2

b)Express the dimentions (in terms of V) of the box so the surface is minimal.

So the surface is given by A=x^2+4xh (since open)

I could replace h from before so A=x^2+4x*(V/x^2) witch is A=x^2+4V/x but I still have a function of two variables.

When I get a funktion of one variable I only need to find the derivative and solve the equation A'(v) or A'(x) equal to 0, but my problem is the two variables.

Acording to the book the results are: x equals the third root of 2v and h=1/2x.

I hope you can help me.

Kind regards

J.

a) Find h expressed by x and V

Easy: V=x^2*h

so h=V/x^2

b)Express the dimentions (in terms of V) of the box so the surface is minimal.

So the surface is given by A=x^2+4xh (since open)

I could replace h from before so A=x^2+4x*(V/x^2) witch is A=x^2+4V/x but I still have a function of two variables.

When I get a funktion of one variable I only need to find the derivative and solve the equation A'(v) or A'(x) equal to 0, but my problem is the two variables.

Acording to the book the results are: x equals the third root of 2v and h=1/2x.

I hope you can help me.

Kind regards

J.