Name: __________________________________
Date: _________________
KWL Chart
In this activity, begin by filling out the first two columns. This will give you an idea of what you
know about the subject. The last column will be completed at end of Lesson 3.
Topic: Interpreting Graphs and Functions Using Calculus
What I Know
1. A graph is increasing
when the slope of a
function is positive.
What I Want to Know
What I Learned
1. How do I find an
absolute maximum
and minimum?
1.
2. Compare and
contrast the
difference between
the critical values
and inflection
points?
2.
3. What does the first
derivative help us
find.
3. The first derivative allows us to find the
critical values and some of the
inflection points.
4. What is the process
of the second
derivative?
4. The process of the second derivative
goes as follows:
a. Take the derivative of f(x) and set it
equal to zero.
b. Find the value of f at all critical
2. A graph is decreasing
when the slope of the
function is negative.
To find the absolute maximum and
minimum we could use the closed
interval method. The closed interval
method requires the following:
a. Finding the critical values of the
function (f) and the values of f at the
critical values.
b. Find the values of f at endpoint [a,
b].
c. The points from steps a & b the has
the largest value of f will be the
absolute maximum and the smallest
will be absolute minimum.
3. A maximum is the
highest point on the
graph along the yaxis
4. A minimum is the
lowest point on the
graph along the yaxis.
5. A graph has a slope
of zero if it is a
straight line along the
horizontal axis.
6. The derivative of a
function gives us the
slope of the initial
function.
Critical Values:
 Can be a maximum, minimum or an
inflection point.
 Can be found by taking the first
derivative.
Inflection Points:
 The point at which a graph goes from
concave up to concave down or
concave down to concave up.
 Can be found by taking the first and
second derivative.
values and end points.
c. Then take the second derivative and
substitute the critical values for x
into f”(x).
d. If the values from part c are larger
than 0 then this is a local minimum.
e. If the values from part c are smaller
than 0 then this is a local maximum.
5. Describe the
difference between
concave up and
concave down.
5.
A continuous graph is concave up
when the slope of a graph goes from
decreasing to increasing. Concave up
means this will look like a happy face.
A continuous graph is concave down
when the slope of the graph goes from
increasing to decreasing. Concave
down means this will look like a sad
face.