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Solutions to a function II

Bushy

Member
Jul 2, 2012
40
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

Active member
Aug 18, 2013
76
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)
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,899
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...