5.2 Increasing and decreasing functions Quiz

1. $f'(2)=-4$. What does this tell you about $f$ at $x=2$?

• A. $f$ is increasing
• B. $f$ has a horizontal tangent
• C. $f$ is decreasing
• D. $f(2)=-4$

2. For $f(x)=x^2-4x$, on which interval is $f$ decreasing?

• A. $x<2$
• B. $x>2$
• C. $x<-2$
• D. $x<4$

3. $f'(x)=(x-1)(x-5)$. Where is $f$ increasing?

• A. $1<x<5$
• B. $x>5$ only
• C. $x<5$
• D. $x<1$ or $x>5$

4. The graph of $f'$ lies below the $x$-axis for $-2<x<4$. What is true of $f$?

• A. $f$ is increasing for $-2<x<4$
• B. $f$ is decreasing for $-2<x<4$
• C. $f$ is negative for $-2<x<4$
• D. $f$ is constant for $-2<x<4$

5. For $f(x)=x^3-3x^2$, on which interval is $f$ decreasing?

• A. $x<0$
• B. $x>2$
• C. $0<x<2$
• D. $x<0$ or $x>2$