Welcome to Derivatives!
Questions Involving Derivatives
• How fast am I going?
• How much more money does my company
earn for each good that I produce?
• At what rate is the population growing in
Indianapolis?
• At what rate are the glaciers melting (for those
who believe in global warming!)?
Q:/ What do these questions have in common?
Today’s AGENDA
• Remediation Reminder
• Derivatives Intro Video: How do Newton,
Leibnitz and Usain Bolt Relate?
• Section 3.1 Notes: Introduction to Derivatives
• IP: Section 3.1 IP.
Benchmark
Announcements/Housekeeping
• You may remediate 1 skill. Please email what
you want to remediate and I can send you
some extra practice.
• Expect the benchmark study guide on
Thursday.
• Expect similar questions to the mastery
assessments.
Outcomes
• SKILL 18: Define Derivatives in your own
words.
• BONUS SKILL: Evaluate Limits using the Limit
Definition of Derivative
+ Not only BONUS points but also helps you
compute limits.
3.1 Notes
• Please take out your 3.1 Notes
• As we watch the video. Please write down key
takeaway points.
• Mr. Benzel reserves the right to stop the video
to highlight key points and ask questions.
Main Takeaways
• The derivative is a function that represents the
slope of a tangent line at a given point.
• Think of the derivative as instantaneous slope.
(i.e. As you are traveling on a highway, the speed
at which you are going is the derivative of the
displacement).
• The best way to approximate the derivative is to
minimize as much as possible the distance
between two points on the graph and draw a line
through it.
Warm Up Question
Illustrative Example Part 1
Illustrative Example 1 CTD
Using Limit Definition of Derivative
Illustrative Example Part 2
Whiteboard
• Use the limit definition of derivative to
compute the derivative of 2x2
Independent Practice
• Please work in your seat. You may collaborate
with those near you.
• Question 1: Interpret in your own words
• Question 2: Review of Slope
• Question 3: Application Problem getting to the
concept of a derivative
• Question 4/5: Limit Definition: Similar to Our
Illustrative Example..