I'm looking at problem #40. Before going further, this is homework, so I don't want the answer. I just want guidance, and if I'm on the wrong track, I want to be pushed in the right direction.
Single Variable Calculus - Problem # 40
So, I'm looking for L1 and L2.
Here is what I'm doing for L1
- Write equation
- Get derivative of equation
- Simplify
- Use Newton's Method to solve
My work for L1
- $$x^5 - (2+r)x^4 + (1+2r)x^3 - (1-r)x^2 + 2(1-r)x + r - 1 = 0$$
- $$ 5x^4 - 4(2+r)x^3 + 3(1+2r)x^2 - 2(1-r)x + 2(1-r) + r = 0 $$
- $$ 5x^4 - 8x^3 + 4rx^3 + 3x^2 + 6rx^2 - 2x - 2rx - 2r + r +2 = 0 $$
I assume after that I fill in the r value and then use Newton's Method to finish it off?
Now for L2
- Write equation
- Get derivative of equation
- Simplify
- Use Newton's Method to solve
Here is what I'm doing for L2
- $$ p(x) - 2rx^2 = 0 $$
- $$ p(x)' - 4rx $$
- $$ 5x^4 - 8x^3 + 4rx^3 + 3x^2 + 6rx^2 - 2x - 6rx - 2r + r +2 = 0 $$
Can someone check my work and tell me whether I'm on the correct track? If I am, do my derivatives look correct?