The problem says: Using the Cauchy's integral formula show that if $f(z)$ is an entire function wich verifies $|f(z)|\leq1+2|z|^3$ $\forall z \in \mathbb{C}$ show taht $f(z)$ is a polynominal and calculate his grade.
It's obvious that is a polynominal because it is entire, so u can use Taylor theorem centered in 0 to show that $f(z)=\sum a_nz^n$ with $a_n=f^n(0)/n!$. But i don't know how to calculate the grade.
Apply Cauchy's Integral Formula to write $f^{(n)}(0)$ as an integral over the circle of radius $R$ around $0$ and use an obvious bound for the integral to get $f^{(n)}(0)=0$ for $n>3$ by letting $R \to \infty $.