Slope Field

▶ Refer to Khan academy: Worked example: range of solution curve from slope field

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Example

Solve:

Example

Solve: Hint: Try a point or points in each quadrant, like Q1: (2,2), Q2: (-2,2), Q3: (-2,-2), Q4: (2,-2)

• Let's only try the point (2, 2), we will get y' = 0, which means the line in Q1 would be horizontal.

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Example

Solve:

• Since 6 is the initial condition, so we make 6 as a boundary.

• The slope at (0,6) is a negative slope, which seems keeps negative until 4.

• So the Range would be (4, 6].

Example

Solve:

• Try out a point, etc, the initial point is (0, 1).

• TAKE DERIVATIVE of each equation, to get the SLOPE of each.

• Plug in the x=0 value to get each slope, and eyeball it.