Problem:
You work for a company that sells candy. You have been asked by your supervisor to design a box for candy that could be made from the 8.5 inch by 11 inch cardboard sheet available in the warehouse. These are to be open top display boxes, produced by cutting and folding the cardboard sheet. Squares are to be cut from each corner and the sides folded up to make the box
Because the candy pieces are small enough to fit in any box you design, you decide to design a box that has the largest volume possible. Your report should include the size of the squares to be removed, the dimesions of the resulting box, the amount the box holds
The mathmeatics supporting your results shoudl include a complete graph of the function, the appropriate use of the first and second defrivativs, and a sign chart of the first and second derivatives. That is use the first derivative to find the critical values of the function and use the second derivative to justify that you found a maximum value of the function.
ok so i come up with the eauqtion of
V= (11-2x)(8.5-2x)(x)
V= 4x^3-39x^2+93.5x
first derivative f'(x)= 12x^2-39x+93.5
then I tried to find the critical values by plugging it in the quadratic formula but then the answer is error. Can you explain what I been doing wrong? and what should I do instead?
~Then what should I do next after I find the critical values?
~Help is appreciated. Thank you
You work for a company that sells candy. You have been asked by your supervisor to design a box for candy that could be made from the 8.5 inch by 11 inch cardboard sheet available in the warehouse. These are to be open top display boxes, produced by cutting and folding the cardboard sheet. Squares are to be cut from each corner and the sides folded up to make the box
Because the candy pieces are small enough to fit in any box you design, you decide to design a box that has the largest volume possible. Your report should include the size of the squares to be removed, the dimesions of the resulting box, the amount the box holds
The mathmeatics supporting your results shoudl include a complete graph of the function, the appropriate use of the first and second defrivativs, and a sign chart of the first and second derivatives. That is use the first derivative to find the critical values of the function and use the second derivative to justify that you found a maximum value of the function.
ok so i come up with the eauqtion of
V= (11-2x)(8.5-2x)(x)
V= 4x^3-39x^2+93.5x
first derivative f'(x)= 12x^2-39x+93.5
then I tried to find the critical values by plugging it in the quadratic formula but then the answer is error. Can you explain what I been doing wrong? and what should I do instead?
~Then what should I do next after I find the critical values?
~Help is appreciated. Thank you
