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Slope Fields

Explore the concept of slope fields through an engaging quiz. You'll calculate the average value of a velocity function over a specified interval, determine derivatives, and analyze differential equations. Learn how these derivatives illustrate the slope at various points, with small line segments depicting sections of the slope at given points. By solving the differential equation, discover how to sketch a possible solution on the slope field. This comprehensive understanding will enhance your grasp of slopes in calculus.

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Slope Fields

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  1. Slope Fields

  2. Quiz • Find the average value of the velocity function on the given interval: [ 3, 6 ] 2) Find the derivative of 3) 4) 5)

  3. Consider the differential equation This derivative represents the slope of the function at any given values of x and y

  4. Small line segments can be drawn to represent small sections of the slope at any given point The result is called a slope field

  5. The solution (integral) of the differential equation represents one possible “shape” of the slope field Example: Solve the differential equation for the specific point and sketch the solution on the slope field

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