## Sallyride666 2 years ago if you have a rectangle that is 10 by 18 and you cut out the corners equally to make it a box how do you maximize the volume and what is the volume?

1. satellite73

first the expression that gives you the volume of the box \[V(x)=x(10-x)(18-x)\] domain will be \((0,5)\) expand, take the derivative, which will be a quadratic, find the critical points by setting it equal so zero and solve for \(x\)

2. satellite73

hope you are good from there, it is basically algebra from here on in

3. Sallyride666

is it a cubic or a quadratic?

4. satellite73

\(V(x)\) is cubic, \(V'(x)\) is degree 2

5. satellite73

ooh damn damn damn i am way wrong!!!

6. Sallyride666

oh sorry forgot to take the derivitive. and should it be x(18-2x)(10-2x) bc you take the corner away from each side?

7. satellite73

sorry about that try \[V(x)=x(10-2x)(18-2x)\] thats better

8. satellite73

yes, you are right, i am way off

9. Sallyride666

10. satellite73

obviously not but in any case algebra gives you \[V(x)=4 x^3-56 x^2+180 x\] and then it should be more or less routine

11. Sallyride666

thanks. if you have a box and the lenghth is 12cm and the width is 5cm and the width is increasing at 2 cm/sec and the length is decreasing at 2 cm/sec what is the DA/dt for the area perimeter and diagonal