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Derivatives – test 3: Monotonicity and extrema

10 multiple-choice and short-answer problems on derivatives (Mathematics I). The solutions are shown after checking.

For multiple-choice questions choose one answer. For the others type the answer: a number, a decimal or a fraction such as 5/12. When you finish, click Check answers.

1. Where does \(f(x)=x^3-3x\) have a local maximum?

2. What is the local minimum value of \(f(x)=x^3-3x\)?

3. How many local extrema does \(f(x)=x^2(2-x)^2\) have?

4. Which is true for \(f(x)=\frac{x}{x^2-1}\)?

5. What is the largest value of \(f(x)=\sqrt{2x-x^2}\)?

6. What is the local minimum value of \(y=\frac{2x-1}{(x-1)^2}\)?

7. On which interval is \(f(x)=e^{-x^2}\) increasing?

8. What is the local minimum value of \(y=\frac{x^2}{x-1}\)?

9. What are the stationary points of \(y=x-1+\frac{3}{x+2}\)?

10. Where does \(f(x)=xe^{-x}\) have a local maximum? Enter \(x\).