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CSS Pure Mathematics QUESTION #1264
Question 1
The Mean Value Theorem states that if \(f\) is continuous on \([a,b]\) and differentiable on \((a,b)\), then there exists \(c\in(a,b)\) such that:
  • f(c) = \dfrac{f(a)+f(b)}{2}
  • f'(c) = \dfrac{f(b)-f(a)}{b-a}✔️
  • f'(c) = f(b)-f(a)
  • f(c) = f(b)-f(a)
Correct Answer Explanation
The Mean Value Theorem (Lagrange) guarantees existence of \(c\in(a,b)\) such that \(f'(c)=\dfrac{f(b)-f(a)}{b-a}\). This means the instantaneous rate of change equals the average rate of change over \([a,b]\).