Long shot but does anyone have experience of using Maxima (maths program) for finding stationary points.
My user guide offers no help, ive tried to manipulate the following derivative to find the stationary points however its not proving helpful.
(9*x^6+28*x^4+51*x^2-88*x-10)/(3*x^2+2)^2
Anyone got any ideas?
If (9*x^6+28*x^4+51*x^2-88*x-10)/(3*x^2+2)^2
is the derivative of some function and you want to find max/min, you would set the above equal to zero
that would leave you with
9x^6 + 28x^4 + 51x^2 - 88x - 10 = 0
I am not at all familiar with your software, but my favourite math website shows two real solutions for the above.
http://www.wolframalpha.com/input/?i=9x%5E6+%2B+28x%5E4+%2B+51x%5E2+-+88x+-+10+%3D+0
See what you can do with this.
Do you have the original function?
if so, plug in the two real solutions
Thanks Reiny,
Ive had a look on wolfram alpha and seen the solutions. My problem is I need to show it using Maxima but for some reason Maxima will not solve my equation 9x^6 + 28x^4 + 51x^2 - 88x - 10 = 0.
So frustrating.
I'm surprised that Maxima gagged on a simple polynomial. I've used it very little, but I know it's been around for over forty years, and was way powerful back in the 70's.
Maybe that pesky 88x term messes things up; otherwise it'd just be a cubic in x^2.
To find the stationary points of a function using Maxima, you can follow these steps:
1. Define the function: Start by defining the function in Maxima. In your case, the function is given as (9*x^6+28*x^4+51*x^2-88*x-10)/(3*x^2+2)^2. You can define it by assigning it to a variable, like f(x):
```
f(x) := (9*x^6+28*x^4+51*x^2-88*x-10)/(3*x^2+2)^2;
```
2. Find the derivative: Use the 'diff' function in Maxima to differentiate the function with respect to x (the variable you want to find the stationary points for). The 'diff' function takes two arguments: the function and the variable with respect to which you want to differentiate. In this case:
```
f_derivative(x) := diff(f(x), x);
```
3. Solve for the derivative: Now that you have the derivative, set it equal to zero and solve for the value(s) of x using the 'solve' function in Maxima. The 'solve' function takes two arguments: the equation and the variable you want to solve for. In this case, the equation is f_derivative(x) = 0:
```
stationary_points : solve(f_derivative(x) = 0, x);
```
The variable 'stationary_points' will now contain the values of x that correspond to stationary points.
Keep in mind that Maxima might return multiple solutions, so make sure to inspect the results to identify any possible stationary points.