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

Friday, February 15, 2019 MAT 145

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

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

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

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

MAT 145

Friday, February 15, 2019 MAT 145

Practice Derivative Rules Friday, February 15, 2019 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, February 15, 2019 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, February 15, 2019

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

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

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

Practice Derivative Rules Friday, February 15, 2019 MAT 145

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