Maximizing a 3rd Order Polynomial: Finding Duplicate Solutions

[Bushy]

Consider the function

f(x) = (x+4)^2(a-x)

Let T be greater than 0, find 'a' such that f(x) = T has 2 solutions.

No idea how to kick this one off..

 

[eddybob123]

Exactly how badly do you need the solution? This is basically a generalization of your previous thread, and that one was already answered by MarkFL, to your dissatisfaction. I don't immediately see another solution, unless you want to use the cubic formula (which I really don't recommend).

(Bandit)

 

[I like Serena]

Consider the function

f(x) = (x+4)^2(a-x)

Let T be greater than 0, find 'a' such that f(x) = T has 2 solutions.

No idea how to kick this one off..

Hi Bushy!

A 3rd order polynomial has only 2 solutions if one of the 2 is a duplicate solution, meaning it has an extreme value there.
To find an extreme value you're supposed to take the derivative...