5.15 Slope fields Quiz

1. A slope field is drawn for $\frac{dy}{dx}=x+y$. Find the gradient of the segment at $(2,-1)$.

• A. $0$
• B. $1$
• C. $2$
• D. $3$

2. A slope field is drawn for $\frac{dy}{dx}=y$. What is true of the segments along the line $y=3$?

• A. All are horizontal
• B. All have gradient 1
• C. Their gradients increase as $x$ increases
• D. All are parallel, with gradient 3

3. For $\frac{dy}{dx}=x(y-2)$, on which lines are the segments horizontal?

• A. $x=0$ and $y=2$
• B. $x=0$ only
• C. $y=2$ only
• D. $x=2$ and $y=0$

4. Why can two solution curves of the same slope field not cross?

• A. Solution curves must be straight lines
• B. Segments exist only at integer points
• C. At the crossing point the field gives only one gradient, but two curves would need two
• D. A solution curve must be horizontal where it crosses another

5. A model has $\frac{dP}{dt}=0.1P(8-P)$. What happens to $P$ at the point where $P=10$?

• A. It increases
• B. It decreases
• C. It stays constant
• D. The gradient is undefined