19. Oppgaver: Polynomer#
Polynomfunksjoner
\[
f(x) = (x - r)(ax^2 + px + q)
\]
Polynomdivisjon
\[
\dfrac{f(x)}{x - r} = K(x) + \dfrac{R}{x - r}
\]
Polynomlikninger
\[
x^3 + 5x^2 - x - 5 = 0
\]
\[
(x - r)(ax^2 + px + q) = 0
\]
\[
x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
Den deriverte
\[
f'(x) = 3ax^2 + 2bx + c
\]
\[
(ax^n + bx^m)' = nax^{n-1} + mbx^{m-1}
\]
\[
y - y_1 = a(x - x_1)
\]
Optimering
\[
f'(x) = 0
\]
\[
A'(a) = 0
\]