Maximizing a 3rd Order Polynomial: Finding Duplicate Solutions

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  • Thread starter Bushy
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But, this one is a bit complicated.In summary, to find the value of 'a' such that f(x) = T has 2 solutions, we need to find the extreme value of the given function, which can be found by taking the derivative of the function. This may be a bit complicated, but it is necessary in order to find the desired value of 'a'.
  • #1
Bushy
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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..
 
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  • #2
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)
 
  • #3
Bushy said:
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...
 

FAQ: Maximizing a 3rd Order Polynomial: Finding Duplicate Solutions

1. What is a solution to a function?

A solution to a function is a value or set of values that make the function true when substituted into the equation. It is the point(s) where the graph of the function intersects with the x-axis.

2. How do you find the solutions to a function?

To find the solutions to a function, you can set the function equal to 0 and then solve for the variable. This will give you the x-values of the points where the function crosses the x-axis.

3. Can a function have more than one solution?

Yes, a function can have more than one solution. This means that there can be multiple points where the function crosses the x-axis and makes the equation true.

4. Are there any shortcuts to finding solutions to a function?

Yes, there are a few shortcuts that can be used to find solutions to a function. These include factoring, using the quadratic formula, and using the graph of the function to estimate the solutions.

5. How do you check if a value is a solution to a function?

To check if a value is a solution to a function, you can substitute the value into the function and see if the resulting equation is true. If it is, then the value is a solution to the function.

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