Slope Fields

The exercise appears under the Differential equations Math section on Khan Academy. This exercise shows the slope fields of differential equations.
==Types of Problems==
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.
==Strategies==
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 \frac{dy}{dx}
# When \frac{dy}{dx} = 0, a horizontal line is produced on a slope field.
# When \frac{dy}{dx} = undefined, a vertical line is produced on a slope field.
==Real-life Applications==
# 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.
Category:Math