6th degree function equation?
Hey people
I have a problem my friend explained to me, and it comes with a solution. I've tried several times to find the answer using a matrix on my calculator, but I always get a different answer.
So 1. You write the operations
2. The derivative
3. Replace X values with the conditions and then you should get the whole thing out with a matrix but … 🙁
This is what I found out:
So the task is:
The graph of a polynomial function of degree 6 is axisymmetric and has a nadir at (0/12) and an inflection point at (1/15). Calculate the function's equation.
Solution check: f(x)=0.5x⁶ – 2x⁴ + 4.5x² +12
It would be great if you could explain the whole thing using the matrix (with individual steps)
Thanks in advance 🙂
(1 votes)
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First, “axis-symmetrical” means that only straight potencies can occur (see solution function). This reduces the number dre unknown coefficients from 7 to 4, a6, a4, a2 and a0. a0 is given by the condition equation f(0)=12 (the function goes through (0|12)). A6, a4 and a2 are still required for the three equations. Now f(1) = 15. The function now formally derive twice, it is f'(0)=0 and f'(1)=0. These are the three equations, now solve the equation system.
Yeah, I got it out, but if I put it on Matrix, I got the wrong solution
If you don’t get the equations you get, it’ll be nothing. No solution without work.
I’m not looking for the question(s) now. But there are many.
in any case, the FS consistently refuses to solve the grease by hand
and adds : there are infinitely many solutions , since the TP has a condition nix because of 0 = 0
we had already, see:
You have already written the matrix is a tool on your calculator and I have already commented on it. Tools only bring something when you know how to use them.
I don’t think you understood my question. Do you know what Matrix means?
The solution is not the only one . There are infinite many .
Because the TP does not provide information because of f'(0)=0
What do you mean, Matrix?
In the calculator there is a button called the matrix and thus such tasks are calculated
No. This means that such tasks are expected if you have fulfilled the requirements. A calculator does not provide mathematics, but only the invoice based on correct mathematical execution.
ok, there we have something concrete. You can’t come to the solution, you should have one of the parameters of the already known (!!!!) accept solution as given
In short, it is not possible.
see what makes a professional program
Apparently your TR IRGENDEINE delivers the infinitely many solutions. What is quite doof,if there is no comment on the display.
I know that there are many solutions but would like to come to this solution that I wrote above in solution control
That’s not a miracle either. Have you already read and understood the comment of @Halbrecht?
So…
f(x) = a * x6 + b * x4 + c * x2 + d
f'(x) = 6 * a * x5 + 4 * b * x3 + 2 * c * x
f”'(x) = 30 * a * x4 + 12 * b * x3 + 2 * c
Conditions:
(1) f(0) = 12
(2) f(1) = 15
(3) f'(0) = 0
(4) f”(1) = 0
LGS:
(1) 12 = d
(2) 15 = a + b + c + 12
(3) 0 = 0
(4) 0 = 30 * a + 12 * b + 2 * c
So when I put the numbers in matrix I get out (see the task position).
Why should I understand that if you don’t even give me your bill, the numbers you used wrongly and what you think are the correct figures?
I didn’t mean the whole solution. So my problem was that I used the wrong numbers ABER doesn’t know what my mistake was that I got those numbers out. But no one understands