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

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Presentation transcript:

Calculus I (MAT 145) Dr. Day Friday September 29, 2017 Derivative Shortcuts (Chapter 3) Sums & Differences, Products & Quotients, and More! (3.1- 3.2) Derivatives of Trig Functions (3.3) Derivatives of Composite Functions (3.4) Friday, September 29, 2017 MAT 145

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

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

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

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

Practice Derivative Rules Friday, September 29, 2017 MAT 145

Friday, September 29, 2017 MAT 145

Friday, September 29, 2017 MAT 145

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

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

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

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

Practice Derivative Rules Friday, September 29, 2017 MAT 145

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