The function $f$ has derivatives of all orders within its radius of convergence of $\frac { 1 } { 3 }$ about $x = 0$ and its Maclaurin series is $\displaystyle\sum _ { n = 0 } ^ { \infty } 3 ^ { n } x ^ { n + 2 }$.

1. Write the first four derivatives of $f$.

   Hint (a):

   Remember, 3ⁿ is just a number, so:

2. Expand the Maclaurin series of $f$ out to four terms. Then find the integral of this polynomial, $p_4(x)$.

   Hint (b):

   $p_4(x)=3^0x^{0+2}+3^1x^{1+2}+3^2x^{2+2}+3^3x^{3+2}$