5. The derivative in graphing and applications - Calculus

Q1. True or false: If \(f'(c)=0\) then \(f\) must be constant on an interval containing \(c\).

💡 Difficulty: easy | ✅ Correct: B

Q2. Is the function \(f(x)=e^{-x}\) increasing, decreasing, or constant on \((-\infty,\infty)\)?

💡 Difficulty: medium | ✅ Correct: B

Q3. Prove: If \(f'(x)>0\) for all \(x\) in \((a,b)\), then \(f\) is increasing on \([a,b]\). Which theorem justifies this statement?

💡 Difficulty: hard | ✅ Correct: A