📝 The Mean Value Theorem

Q1. If \(f(x)=x^3-3x+2\) on \([0,2]\), which point \(c\) guaranteed by the Mean Value Theorem satisfies \(f'(c)=\dfrac{f(2)-f(0)}{2-0}\)?

💡 Difficulty: easy | ✅ Correct: B

Q2. A car travels from mile marker 10 to mile marker 70 in 1 hour. Which statement follows from the Mean Value Theorem applied to its position function?

💡 Difficulty: medium | ✅ Correct: A

Q3. A manufacturing process yields output \(Q(t)=t^4-8t^3+18t^2\) units per day for \(t\) in days from 0 to 4. Which day must satisfy the Mean Value Theorem?

💡 Difficulty: hard | ✅ Correct: B