Equations of Tangent Lines

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Presentation transcript:

Equations of Tangent Lines

Objective To use the derivative to find an equation of a tangent line to a graph at a point. TS: Explicitly assessing information and drawing conclusions.

Equations of Tangent Lines Find the equation of the tangent line to

Equations of Tangent Lines

Equations of Tangent Lines Find the equation of the tangent line to Slope of f(x) at any x value Slope of the tangent line at (7, 15)

Equations of Tangent Lines We now have the slope and a point. We want the equation of the line with slope of 9 and going through (7,15).

Equations of Tangent Lines Find the equation of the tangent line to

Equations of Tangent Lines

Equations of Tangent Lines

Equations of Tangent Lines Find the equation of the tangent line to Slope of f(x) at any x value Slope of the tangent line at x = 4

Equations of Tangent Lines We now have the slope and the x-coordinate of a point. We first need to get the y-coor, then we will have both the slope and the point for our line.

Conclusion The derivative is a formula used to find the slope of the tangent line to a function. To find the slope of the tangent line to a function, first, find the derivative and, second, plug the corresponding x-value into the derivative. To write an equation for the tangent line, use the derivative value (the slope), and the corresponding point on the function.