AMO 2024 – Secondary 4 (Grade 10) Question 7

Let $f(x)=x^2-5x-14$. Points $A=(2,f(2))$ and $B=(2+\Delta,f(2+\Delta))$ lie on its graph, where $\Delta\ne0$. As $\Delta$ approaches zero, what value does $R=[f(2+\Delta)-f(2)]/\Delta$ approach?