5.10 Second derivative and concavity

5.10 Second derivative and concavity Quiz

IB Maths: Applications and Interpretation HL: Quiz

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5 questions, one answer each

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1. Find $f''(x)$ for $f(x)=x^3-3x^2$ .
- A. $3x^2-6x$
- B. $6x-6$
- C. $6x$
- D. $6$
2. For $f(x)=x^3-3x^2$ , which statement is true?
- A. $f$ has a maximum at $x=2$
- B. $f$ has a minimum at $x=0$
- C. $f$ has a point of inflexion at $x=2$
- D. $f$ has a minimum at $x=2$
3. On an interval where $f''(x)<0$ , the graph of $f$ is
- A. concave-down
- B. concave-up
- C. always increasing
- D. always decreasing
4. A point of inflexion requires
- A. $f'(x)=0$
- B. $f''(x)=0$ only
- C. $f''(x)$ to change sign
- D. $f''(x)>0$
5. At a stationary point $f''(x)=0$ . What does the second derivative test tell you?
- A. A minimum
- B. It is inconclusive; check the sign of $f'$
- C. A maximum
- D. A point of inflexion always