Example 2: The Slope of the Graph of a Nonlinear Function. Find the slope of the tangent lines to the graph of . 3. Vertical Tangent The definition of a tangent line to a curve does not cover the possibility of a vertical tangent line. For vertical tangent lines, it’s possible to use this definition: Definition of a Vertical Tangent Line If is continuous at and c, , The vertical line passing through is a x = c vertical tangent line to the graph of f. Definition of the Derivative of a Function The of at is given by derivative f x provided the limit exists. For all for which the limit exists, is a function of x x. The process of finding a derivative is called differentiation. Written as an imperative verb, it would be differentiate. A Side Note on “Notation” In addition to , is read prime of x,” other notations are used to denote the derivative of . The most “f common are: Whenever we read the second one above, we say derivative of y with respect to x.” “the
Example 2: The Slope of the Graph of a Nonlinear Function. Find the slope of the tangent lines to the graph of . 3. Vertical Tangent The definition of a tangent line to a curve does not cover the possibility of a vertical tangent line. For vertical tangent lines, it’s possible to use this definition: Definition of a Vertical Tangent Line If is continuous at c, and , The vertical line x = c passing through is a vertical tangent line to the graph of f. Definition of the Derivative of a Function The derivative of f at x is given by provided the limit exists. For all x for which the limit exists, is a function of x. The process of finding a derivative is called differentiation. Written as an imperative verb, it would be differentiate. A Side Note on “Notation” In addition to , is read “f prime of x,” other notations are used to denote the derivative of . The most common are: Whenever we read the second one above, we say “the derivative of y with respect to x.”
Section%202.1%20-%20Definition%20of%20Derivative%20and%20Differentiability.docx