2 Curve C has equation y = f(x) Curve C has equation y = f(x). To calculate the slope of a secant segmentfrom point P to point Q, we use
3 But what if we want the EXACT slope of the tangent line at point P??? DEFINITION: The tangent line to the curve y = f(x) at the point P (a, f(a))Is the line through P with slopeExample: Find an equation of the tangent line to the parabolaat the point P (1,1)
4 We can also use the following (similar) equation for slope: Find an equation of the tangent line to the hyperbola at the point (3,1)
5 Velocity: Average velocity Instantaneous velocity
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