Types of ProblemsEdit
There are six types of problems in this exercise:
- Which of the following differential equations generates the slope field pictured below: The student is asked to find the differential equation that would create the given slope field.
- Which of the following slope fields is generated by the differential equation: The student is asked to find the slope field that is created by the differential equation.
- Which of the following is the general solution to the differential equation: The student is asked to determine the solution to the differential equation given the slope field.
- Which of the following is the range of the solution curve: The student is asked to find the range of the solution curve given the initial condition.
- What short segment of slope would you draw: The student is asked to determine what short segment of slope should be drawn at the given point.
- Match each slope field on the right with its generating differential equation on the left: The student is asked to match the slope field with its differential equation.
Knowledge of derivatives, differential equations, and slope fields are encouraged to ensure success on this exercise.
- When finding the general solution to the differential equation that generated the given slope field, pick any segment on the slope field and, using the direction of the segment, draw a particular solution to the differential equation used to create this slope field.
- The horizontal asymptotes on a slope field can help determine the range of the function at the initial condition by eliminating choices.
- Finding the short segment of slope for a differential equation can be down by substitution of the given x and y-coordinates into
- When , a horizontal line is produced on a slope field.
- When = undefined, a vertical line is produced on a slope field.
- Computers and calculators use slope fields to numerically find graphical solutions.
- Slope fields are used to make sure the wing-load of an airplane does not get too high.