x

$f\left(x\right)$

$f^{\prime }\left(x\right)$

$f^{″}\left(x\right)$

$-f^{‴}\left(x\right)/12$

0

0

0

2

1

1/3

5/90 = 1/18

5/24 = 0.208333

−5/16 = −0.31250

(3/4)⁴

1/2

1/12

1/9

−22/27 = −0.8148148

(2/3)⁴

$\phi$

${\phi }^5$

0

$-\left(1+{\phi }^6\right)$

${\phi }^4$

1

0

−1/2

−3/2

(1/2)⁴