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Emma Wagner

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a is a point on f(x)
The tangent line of a is shown by the red line
The slope of the tangent line of a is the derivative of a
When you zoom in on a parabola point on a calculator, it becomes linear

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The rate at which something falls

The rate at which someone burns calories while on stationary equipment

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- To determine speed like (miles per hour)
-to determine population growth/ spread of diseases

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Slope of tangent line from curve

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Anna Leland

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you find the instantaneous velocity,

- limit of the slope average as it approaches 0

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The derivative is equivalent to the instantaneous velocity.

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The derivative is the line tangent to (a,f(a)). The points selected on the graph will have a slope of zero.

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The instantaneous velocity

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Derivatives can apply in a number of contexts, such as the rate at which water flows out of a tank, the rate at which calories are burned on a stationary bike, the or the velocity of a falling object (and how those respective rates/velocities change).