3.1 Definition of the Derivative & Graphing the Derivative

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Presentation transcript:

3.1 Definition of the Derivative & Graphing the Derivative

These are all ways to denote the derivative f prime of x or the derivative of f(x) f prime or the derivative of f y prime dy dx or the derivative of y with respect to x dy dx or the derivative of f with respect to x d dx of f at x or the derivative of f at x

The derivative of a function f with respect to the variable x is the function f’ whose value at x is Provided the limit exists

Find the equation of the derivative using the definition of the derivative

Find the equation of the derivative using the definition of the derivative

Find the equation of the derivative using the definition of the derivative

Find the equation of the tangent line to f(x) at x=2

Graph of Derivative

Graph the derivative

Graph the derivative m=0 m= 15 m= -5 m=10 m= -6 m= 0 m= 8 m=17