# Using differentials to estimate the maximum possible error

1. Apr 23, 2016

### whatphysics

1. The problem statement, all variables and given/known data
Consider a closed rectangular box with a square base of side 3cm and height 5cm. If the side is measured with an error at most 0.02cm and the height is measured with an error at most 0.01cm, use differentials to estimate the maximum possible error in computing the volume of the box.

2. Relevant equations
Volume of the box = [x][/2] * [y][/2] , x base side, y height

3. The attempt at a solution
▽f(x,y) = x^2y + 2xy , x^2 * ((1+y))

and i am unsure of how i can move on from here! do i sub in the x and y values 3 and 5? or the error 0.02 and 0.01 respectively?

thank you!

2. Apr 23, 2016

### vela

Staff Emeritus
What does this mean?

Not sure what you've done here either.

You want to express the differential df in terms of dx and dy.

3. Apr 23, 2016

### Staff: Mentor

I'm as mystified as vela is by what you have here. It's given that the box has a square base. The volume of a rectangular box is the area of the base times the height.
???
Where does this come from?
You don't want the gradient -- you want the differential of the volume, dV.

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