Convex and concave curves and points of inflection Quiz

1. A curve has $f''(x)>0$ on an interval. What is true of the curve there?

• A. It is concave
• B. It is convex
• C. It is decreasing
• D. It has a maximum

2. Why does $y=x^{3}$ have a point of inflection at $x=0$?

• A. Because $f'(0)=0$
• B. Because $f(0)=0$
• C. Because $f''(x)=6x$ changes sign at $x=0$
• D. Because $f'''(0)=0$

3. What is the origin on the curve $y=x^{4}$?

• A. A minimum
• B. A maximum
• C. A point of inflection
• D. Not stationary

4. A curve has $f''(x)=6x-6$. For which values of $x$ is it concave?

• A. $x>1$
• B. $x>0$
• C. $x<0$
• D. $x<1$

5. Which condition is needed for a point of inflection at $x=a$?

• A. $f'(a)=0$
• B. $f''(a)=0$ and $f''$ changes sign at $a$
• C. $f''(a)>0$
• D. $f''(a)=0$ only