Given $f(x)=cx^3-9x+3$ and $f(2)=9$, find the value of $c$.
To find the value of $c$, I need to use the information that $f(2)=9$. That means I can plug in $x=2$ into the function and set it equal to $9$. So I get $f(2)=c(2)^3-9(2)+3=9$. Simplifying this equation, I get $8c-15=9$. Adding $15$ to both sides, I get $8c=24$. Dividing both sides by $8$, I get $c=3$. 