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AMO 2025 – Secondary 4 (Grade 10) Question 7

AMO · AMO 2025 – Secondary 4 (Grade 10)

Question 7

Let $g(x)=2026x^2-2025x+4051$. Points $A=(1,g(1))$ and $B=(1+\delta,g(1+\delta))$ lie on its graph, where $\delta\ne0$. As $\delta$ approaches zero, what does $[g(1+\delta)-g(1)]/\delta$ approach? Source clarification: the printed coordinate of B uses undefined f instead of g, and an extra comma and $\delta$ follow the definition; the graph and displayed ratio specify g as used here.

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  1. 2007
  2. 2020
  3. 2027
  4. 2028