Derivatives Using the Limit Definition

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Presentation transcript:

Derivatives Using the Limit Definition At the end of this lesson you should be able to use the limit definition to find the derivative of a function. find the slope of a tangent line to a given point.

The derivative of with respect to x is the function and is defined as,

Steps to follow Find f(x+h) Simplify f(x+h)-f(x) Put all over h Solve the limit

Examples Find the derivative of the following function using the limit definition of a derivative.

Now use the limit definition

Example 2

Find the slope of the tangent line to at the point (2,3) The derivative IS the slope of the tangent line, so to find it just plug the x-value of the point into the derivative. So the slope will equal 2(2)-3 = 1

Example 3 Find the slope of the tangent line at the point (-1,.5) for

Example 4 Find the derivative of the function Use the conjugate

Practice Problems

Answers f’(x) = 2x-2 f’(x)=

Homework Pg. 770 #6-12 even, 26,28,30,31