# Thread: Finding a maximum X value for equation.

1. ## Finding a maximum X value for equation.

Im having a hard time finding a maximum value. Well, i can find it, but its not the correct value.

Here is the problem:

A rectangular piece of cardboard measuring 26 inches by 47 inches is to be made into a box with an open top by cutting equal size squares from each corner and folding up the sides. Let X represent the length of each side of each such square. For what value of X will the volume be a maximum ?

So Im thinking the equation is set up like this:

(26-2x)(47-2x)(x)=V

And after foiled out:

x(4x^2-146x+1222)

and then I apply vertex formula to get the x value: -b/2a= 146/8= 18.25

Wouldnt 18.25 be the x value? Its says the correct answer is 5.37. What am I doing wrong?

2. Originally Posted by Jerry99
Im having a hard time finding a maximum value. Well, i can find it, but its not the correct value.

Here is the problem:

A rectangular piece of cardboard measuring 26 inches by 47 inches is to be made into a box with an open top by cutting equal size squares from each corner and folding up the sides. Let X represent the length of each side of each such square. For what value of X will the volume be a maximum ?

So Im thinking the equation is set up like this:

(26-2x)(47-2x)(x)=V

And after foiled out:

x(4x^2-146x+1222)

and then I apply vertex formula to get the x value: -b/2a= 146/8= 18.25

Wouldnt 18.25 be the x value? Its says the correct answer is 5.37. What am I doing wrong?
Dear Jerry99,

I noticed that this is in the pre-calculus sub forum. The equation you have is a cubic not a quadratic and will need Calculus (the derivative ) to find its max volume. You could also graph the cubic and find is maximum value that way but it would only be an estimate.

3. Im having a hard time finding an appropriate viewing window on my calculator to see this functions maximum. Any suggestions?

4. Originally Posted by Jerry99
Im having a hard time finding an appropriate viewing window on my calculator to see this functions maximum. Any suggestions?
x should go from 0 to 13 and y should go from 0 to 3000. you may want to scale your y axis in 500 or so as well.

5. thanks for the help