Unit 7.1-7.4, Slope Fields

y' =

dy/dx (x,y)

dy/dx = 0

-

y' =

dy/dx (x,y)

dy/dx = 0

-

dy/dx > 0

/

dy/dx < 0

\

dy/dx = undefined

|

Steps to solving a slope field problem

1) Given a slope field and an initial condition, sketch the general solution to that given initial condition.

2) Look at the answer choices and analyze the parent function geographically.

3) Look for horizontal and vertical asymptotes on the slope field.

4) Identify the correct general solution.

A slope field is...

the graphical representation of a differential equation

When the equation only contains a y variable, you will get repeated...

rows

When the equation only contains a x variable, you will get repeated...

columns

Given one point of the particular solution curve, you can...

sketch the graph from that point, in both directions all the way out of the slope field.

Vertical segments occurs when the equation is...

undefined

What is hiding in the slope fields?

The antiderivative.

A line segment that is 45°-90° always has a slope that is...

greater than 1

A line segment that is <45° always has a slope that is...

less than 1

Rate =

Derivative

Directly proportional to...

=k multiplied to...

Inversely proportional to...

=k divided to...