2.1 The Derivative and The Tangent Line Problem Slope of a Tangent Line.

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2.1 The Derivative and The Tangent Line Problem Slope of a Tangent Line

How do we find the equation of the tangent line at point x? - we need to find the slope of the tangent line, m tan =f’(x)

We can find the slope of a secant line and then take the limit as h approaches 0.

Definition of Tangent Line The slope of the tangent line to the graph of f, at point (x, f(x)) is given by:

Ex) Find the slope of the tangent line to the Graph of the function at the given point. Plan: 1)Find the slope of the tangent line to the graph at any point (x,f(x)) 2)Find the slope when x=-2.

Ex) Find the equation of the tangent line to the graph of the function at the given point. Plan: 1)Find the slope of the tangent line to the graph at any point (x,f(x)) 2)Find the slope when x=5. 3)Write a point slope equation.

Ex) Find the equation of the tangent line to the graph of the function and parallel to the given line. Plan: 1)Find the slope of the tangent line to the graph at any point (x,f(x)) 2)Find the slope of the given line, m. 3)Set equal and solve for x. 4)Find the point of intersection. 5)Write a point slope equation.