Given the extrema and a POI, can we find the cubic equation (3.4 #61 page 196)?

 Given the extrema and a POI, can we find the cubic equation (3.4 #61 page 196)?

Using a Table of Slopes to Sketch a Graph(3.3 #73)

 Using a Table of Slopes to Sketch a Graph(3.3 #73)

Using what we know about the first derivative we can sketch a graph from a table of slopes.  I also show how to put the table into your calculator to see a graph of f'.

Graphing the Derivative from the graph of a f (3.3 # 59, p.188)

 Graphing the Derivative from the graph of a f (3.3 # 59, p.188)

The first derivative to a piecewise function (3.3 p.187 #39)

 The first derivative to a piecewise function (3.3 p.187 #39)

First Derivative, Increasing, Decreasing, and extrema (3.3 (p187) #11, 15, 17, 27, 35

 First Derivative, Increasing, Decreasing, and extrema (3.3 (p187) #11, 15, 17, 27, 35

The first derivative can find relative extremes when it changes from negative to positive (min) or positive to negative (max).  Here are 5 quick examples:

#11 -  0:00

#15 - 2:11

#17 - 3:28 

#27 - 6:00

#35 - 8:08

Another MVT example (3.2 #41)

Another MVT example (3.2 #41)

Another example of using the MVT and finding the place where the instantaneous slope matches the average (mean) slope.

Mean Value Theorem with a Calculator (3-2 #37)

 Mean Value Theorem with a Calculator (3-2 #37)

A basic polynomial to show what the MVT says and how to check your work with a TI-84 style calculator.