2.1 Tangents & Velocities.

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Presentation transcript:

2.1 Tangents & Velocities

Secant Line: a line that intersects a curve at two points, P & Q Secant Line: a line that intersects a curve at two points, P & Q. Slope = Average Rate of Change between P & Q

Tangent Line: a line that intersects a curve at a point P & whose slope approximates the behavior of the curve at or very close to point P. Slope = Instantaneous Rate of Change at P

Average Velocity: the slope of the secant line between two points, P & Q, on a position curve.

Instantaneous Velocity: the slope of the tangent line to a point P on a position curve.

Ex 1: t: sec 1 2 3 4 5 s(t): ft 10 32 70 119 178 Use the data to calculate the slope of the secant line between each of the given points and the point: (3, 70).

Ex 1: Graph the data Estimate the slope of the tangent line @ t = 3 sec From secant lines From graph Find the equation of the tangent line @ t = 3 sec

HW – pg. 89 #1 – 7 odds