Home > APCALC > Chapter 10 > Lesson 10.1.3 > Problem10-35

10-35.

For each of the following differential equations, answer the questions below..

This occurs when the derivative is a maximum.

This can be revealed by sketching the slope field.

• i. When is $y(t)$ changing the fastest?

• ii. What is $\lim\limits _ { t \rightarrow \infty } y ( t )$?

• iii. Sketch a slope field.

1. $\frac { d y } { d t } = 2 y ( 1 - y )$

1. $\frac { d y } { d t } = 2 y - y ^ { 2 }$

Use the eTool below to generate the slope fields.
Click the link at right for the full version of the eTool: Slope Field Generator