1. Calculus I (MAT 145) Dr. Day Friday February 15, 2019
Derivative Shortcuts (Ch 3)
Sums, Differences, Product, Quotients
Constants, Powers, Exponential Functions
Trig Functions
Quiz #5 Today!
Info from a graph: limits, function values, derivatives
Asymptotes defined by limits
Calculate a derivative using the Limit Definition
Contextual Meaning of the derivative
Friday, February 15, 2019
MAT 145

2. Friday, February 15, 2019
MAT 145

3. Now we have a derivative function f that will be true for any x value where a derivative exists!
Friday, February 15, 2019
MAT 145

4. Here is the graph of a function f. Use it to sketch the graph of f ’.
Friday, February 15, 2019
MAT 145

5. Sums, differences, exponentials, & products of constants and functions
Friday, February 15, 2019
MAT 145

6. Derivatives of Trig Functions
Friday, February 15, 2019
MAT 145

7. MAT 145

8. Friday, February 15, 2019
MAT 145

9. Practice Derivative Rules
Friday, February 15, 2019
MAT 145

10. Using Derivative Patterns
For f(x) = 2x2 – 3x + 1:
Calculate f’(x).
Determine an equation for the line tangent to the graph of f when x = −1.
Determine all values of x that lead to a horizontal tangent line.
Determine all ordered pairs of f for which f’(x) = 1.
Friday, February 15, 2019
MAT 145

11. Using Derivative Patterns
MAT 145
Suppose s(x), shown below, represents an object’s position as it moves back and forth on a number line, with s measured in centimeters and x in seconds, for x > 0.
Calculate the object’s velocity and acceleration functions.
Is the object moving left or right at time x = 1? Justify.
Determine the object’s velocity and acceleration at time x = 2. Based on those results, describe everything you can about the object’s movement at that instant.
Write an equation for the tangent line to the graph of s at time x = 1.
Friday, February 15, 2019

12. Using Derivative Patterns
Determine the equation for the line tangent to the graph of g at x = 4.
Determine the equation for the line normal to the graph of g at x = 1.
At what points on the graph of g, if any, will a tangent line to the curve be parallel to the line 3x – y = –5?
Friday, February 15, 2019
MAT 145

13. Warm up! . Find the derivatives. Use correct notation!
Friday, February 15, 2019
MAT 145

14. Practice Derivative Rules - Answers
Friday, February 15, 2019
MAT 145

15. Practice Derivative Rules
Friday, February 15, 2019
MAT 145

16. Practice Derivative Rules - Answers
Friday, February 15, 2019
MAT 145