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Calculus I (MAT 145) Dr. Day Friday September 29, 2017

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1 Calculus I (MAT 145) Dr. Day Friday September 29, 2017
Derivative Shortcuts (Chapter 3) Sums & Differences, Products & Quotients, and More! ( ) Derivatives of Trig Functions (3.3) Derivatives of Composite Functions (3.4) Friday, September 29, 2017 MAT 145

2 Function Graphs and Their Derivatives
Friday, September 29, 2017 MAT 145

3 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, September 29, 2017 MAT 145

4 Sums, differences, exponentials, & products of constants and functions
Friday, September 29, 2017 MAT 145

5 Derivatives of Trig Functions
Friday, September 29, 2017 MAT 145

6 Practice Derivative Rules
Friday, September 29, 2017 MAT 145

7 Friday, September 29, 2017 MAT 145

8 Friday, September 29, 2017 MAT 145

9 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, September 29, 2017

10 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, September 29, 2017 MAT 145

11 Warm up! . Find the derivatives. Use correct notation!
Friday, September 29, 2017 MAT 145

12 Practice Derivative Rules - Answers
Friday, September 29, 2017 MAT 145

13 Practice Derivative Rules
Friday, September 29, 2017 MAT 145

14 Practice Derivative Rules - Answers
Friday, September 29, 2017 MAT 145

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