Need help solving this equation (may be factoring)?

Hi, in math class, we were assigned a challenge problem that has to do with finding the volume of a box. My function is:

f(x) = 4x^{3} - 88x^{2} + 480x

I found that the maximum value of this function is 768 (the maximum volume), but I want to know how to solve for `x`. This is what I have:

768 = 4x^{3} - 88x^{2} + 480x

192 = x^{3} - 22x^{2} + 120x

How would I continue to solve for `x`?

Re: Need help solving this equation (may be factoring)?

How did you get your answer of 768? It should actually be about 774 by the way.

Have you learnt about differentiation?

Re: Need help solving this equation (may be factoring)?

Quote:

Originally Posted by

**Flurite** Hi, in math class, we were assigned a challenge problem that has to do with finding the volume of a box. My function is:

f(x) = 4x^{3} - 88x^{2} + 480x

I found that the maximum value of this function is 768 (the maximum volume), but I want to know how to solve for `x`. This is what I have:

768 = 4x^{3} - 88x^{2} + 480x

192 = x^{3} - 22x^{2} + 120x

How would I continue to solve for `x`?

how did you find that the maximum volume is 768?

I get approximately 774.

Re: Need help solving this equation (may be factoring)?

I used my graphing calculator, but then I just realized that decimals are involved too. All I need is the `x` value and I can't find that in my table.

Re: Need help solving this equation (may be factoring)?

graph the volume and find the maximum ... it will give you the max volume (y-value) and x-value where that maximum occurs.

Re: Need help solving this equation (may be factoring)?

Found out how to change the maximum and minimum values to shift where the graph is showing. Thanks all!