2)a) On the given of f sketch a line whose slope is (f(4)-f(1)/4-1) label the line L1.

Solution:

a) postive number, derivative is 256.

b) derivitive should not exist although the calculator gives you an answer you must discard it because *the calculator is stupid.*

c) horizontal line, slope is zero.

*derivative- to find the slope of tangent line.

Mr.K then handed out a worksheet on The Derivative Function which is to be done for homework.

Here are the questions from the worksheet...

**Investigation 1**

Consider the function f(x)= x^2-2. Using your calculator, graph the function. Using the [DRAW]:[Tangent] feature, calculate the slope of the tangent line for x= -3, -2, -1, 0, 1, 2, 3.

Consider the relationship between x(the values in the first row) and the slope of the tangent (the values in the third row). Find a function (f '(x)) that relates the tow rows in the table. Use your calculator to graph both functions.

**Investigation 2**

Consider the graph below. Estimate the slope (the derivitive) of f for all integral values of x illustrated. Plot these new ordered pairs (f ') on top of the given graph.

**Investigation 3**

Consider the table of values below. Use the data in the table and the difference quotient to estimate the value of f '(x) for each given value of x. Complete the table of values for f '(x).

Use the statistical graphing feature of your calculator to plot both table of values as broken line graphs.

**Investigation 4**

The derivative of a function f(x) can be defined as the limiting value of the difference quotient as h approaches 0: f '=lim(h->0) ( f(x+h)-f(x) )/h. Use this definition to determine the derivative of f(x)=1/x algebraically. Use your calculator to graph both functions.

Tomorrow's scribe is Katrin =)

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