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Derivative Application ,[object Object],[object Object]

Tangent line equation ,[object Object],What do you need to find a tangent line equation? m= Slope of the tangent line (x,y): coordinate of a point (x 1 ,y 1 ): coordinate of another point The slope and a point

[object Object],[object Object],[object Object],[object Object],[object Object],Derivative Applications of tangent line

Derivative Applications of tangent line (cont) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Slope at a point ,[object Object]

Slope at a point ,[object Object],[object Object]

Approximation ,[object Object],[object Object],[object Object],[object Object],[object Object],x 1 2 3 y 4 6 8

Implicit Differentiation ,[object Object],Derive: y 3 + y 2 - 5y -x 2 = -4 1. y 3 + y 2 - 5y -x 2 = -4 2. (d/dx) [y 3 + y 2 - 5y -x 2 ] = (d/dx) -4 3. 3y 2 (dy/dx) + 2y(dy/dx) - 5(dy/dx) - 2x = 0 4. (dy/dx)(3y 2 + 2y -5) = 2x 5. (dy/dx) = 2x/(3y 2 + 2y -5)

Guidelines for Implicit Differentiation ,[object Object],[object Object],[object Object],[object Object]

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