The Derivative Obj: Students will be able to notate and evaluate derivatives.

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Presentation transcript:

The Derivative Obj: Students will be able to notate and evaluate derivatives

The Derivative: It is the slope of the tangent at any x-value It is the INSTANTANEOUS slope of a point The derivative of a function IS a function f’(x) whose value at x is

Alternate Definition The derivative of a function f at the point x = a is

Example: Slope at a point Find the slope of the function f(x) = 2x 2 + 3x at the point (-2, 2)

Example Find f’(x) for f(x) = 2x 2

Treating f’(x) as a function You can use the derivative function to find the slope at ANY point on f(x) Ex: Find the slope at x=3 for f(x) = 2x 2 Ex: Find the slope at x= 6 for f(x) = 2x 2

Example Con’t.d Ex: Find the slope at x= 6 for f(x) = 3x 2 + x

Notations NotationHow to read F’(x)“f prime of x” Y’“y prime” dy/dx “dy dx” “the derivative of y with respect to x” df/dx “df dx” “the derivative of f with respect to x” d/dx f(x) “d dx of f at x” “The derivative of f at x”

HOMEWORK PP {1-3, 5-12, 17, 18}