Thread: 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) = 4x³ - 88x² + 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 = 4x³ - 88x² + 480x
192 = x³ - 22x² + 120x

How would I continue to solve for `x`?

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

Have you learnt about differentiation?

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) = 4x³ - 88x² + 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 = 4x³ - 88x² + 480x
192 = x³ - 22x² + 120x

How would I continue to solve for `x`?

how did you find that the maximum volume is 768?

I get approximately 774.

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.

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

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