1. 3.1 Section 2.2 Average and Instantaneous Rate of Change
The Derivative of a Function at a Point
3.1

2. A look at the definition of the first derivative at a point in action
Note: Scroll down for the second

3. Given the graph below, where does the derivative NOT exist?

4. Let f(x) = ln x
a) Find the average rate of change of f between
x = 0.99 and x = 1.
b) Find the average rate of change of f between
x = 1 and x = 1.01.
c) Explain why the answer in (a) is to large of an estimate
for f ‘ (x) and the answer in (b) is too small of an
estimate for f ‘ (x).

5. Let f(x) = ln x
Find the average rate of change of f between
x = 0.99 and x = 1
x = 1 and x = 1.01

6. Let f(x) = ln x
a) The average rate of change between x = 0.99 and x = 1
is 1.005
b) The average rate of change between x = 1 and x = 1.01
is 0.995
c) Explain why the answer in (a) is to large of an estimate
for f ‘ (x) and the answer in (b) is too small of an
estimate for f ‘ (x).
(a) is too large and
(b) is too small because
f(x) is concave down.