AMO 2023 – Junior College (Grade 11–12) Question 9

Let $f(x)=3x^2-2x+5$, $A=(3,f(3))$, and $B=(3+\delta,f(3+\delta))$ for small nonzero $\delta$. As $\delta\to0$, what value does $R=\frac{f(3+\delta)-f(3)}{\delta}$ approach?