5.2 Increasing and decreasing functions Quiz

1. $f'(x)=x^{2}-9$. On which interval is $f$ decreasing?

• A. $x<-3$
• B. $-3<x<3$
• C. $x>3$
• D. $x<3$

2. The graph of $y=g'(x)$ lies above the $x$-axis for all $x>0$. What can you say about $g$?

• A. $g$ is decreasing for $x>0$
• B. $g(x)>0$ for $x>0$
• C. $g$ is increasing for $x>0$
• D. $g$ has a maximum for $x>0$

3. For $f(x)=2x^{3}+6x$, which is true?

• A. $f$ is decreasing for $x<0$
• B. $f$ is increasing for all $x$
• C. $f'(0)=0$
• D. $f$ has two turning points

4. At $x=2$, $f'(2)=0$ and $f'(x)<0$ on both sides of $x=2$. What happens at $x=2$?

• A. Local maximum
• B. Local minimum
• C. Horizontal tangent, $f$ still decreasing
• D. $f(2)=0$

5. $f(x)=x^{2}-8x$. Where is $f$ increasing?

• A. $x>8$
• B. $x>4$
• C. $x<4$
• D. $0<x<8$