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Derivatives – test 4: Convexity, inflection and asymptotes

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. What is the \(x\)-coordinate of the inflection point of \(y=\frac{2x-1}{(x-1)^2}\)?

2. What is the oblique asymptote of \(y=\frac{x^2}{x-1}\)?

3. What is the horizontal asymptote of \(y=e^{-1/x^2}\)?

4. How many vertical asymptotes does \(y=\frac{x}{x^2-1}\) have?

5. Where are the inflection points of \(y=e^{-x^2}\)?

6. Which is true for \(y=\ln(x^2-1)\)?

7. The oblique asymptote of \(y=\frac{x^3}{(x-1)^2}\) is \(y=x+n\). What is \(n\)?

8. What does the graph of \(y=\frac{x^3-1}{x^2+x-2}\) have at \(x=1\)?

9. How many inflection points does \(y=x^2(2-x)^2\) have?

10. What is the \(x\)-coordinate of the inflection point of \(y=(1-x)e^x\)?