Calculus I (MAT 145) Dr. Day Wednesday February 13, 2019 The limit definition of derivative (2.8) Properties and Characteristics of Derivatives (2.8) Derivative Shortcuts (Ch 3) Quiz #5 on Friday! Info from a graph: limits, function values, derivatives Asymptotes defined by limits Calculate a derivative using the Limit Definition Contextual Meaning of the derivative Wednesday, February 13, 2019 MAT 145
The function f ’(x) is called: the derivative of f at x, the instantaneous rate of change f at x, the slope of f at x, and the slope of the tangent line to f at x. Wednesday, February 13, 2019 MAT 145
Wednesday, February 13, 2019 MAT 145
Now we have a derivative function f that will be true for any x value where a derivative exists! Wednesday, February 13, 2019 MAT 145
Here is a graph of the function y = g(x) Here is a graph of the function y = g(x). Arrange the following values in increasing order. Explain your process and determination. Wednesday, February 13, 2019 MAT 145
Here is the graph of the function y = |x|. Why does the derivative NOT exist at x = 0? Wednesday, February 13, 2019 MAT 145
Three situations for which a derivative DOES NOT EXIST! Wednesday, February 13, 2019 MAT 145
For each graphed function, state points at which the function is NOT differentiable. Explain your choices! Wednesday, February 13, 2019 MAT 145
Function Graphs and Their Derivatives http://www.maa.org/sites/default/files/images/upload_library/4/vol4/kaskosz/derapp.html Friday, Sept 21, 2018 MAT 145
Match each function, a-d, with its derivative, I-IV. Wednesday, February 13, 2019 MAT 145
Identify each curve. Explain your choices. Here are the graphs of four functions. One repre- sents the position of a car as it travels, another represents the velocity of that car, a third repre- sents the acceleration of the car, and a fourth graph represents the jerk for that car. Identify each curve. Explain your choices. Wednesday, February 13, 2019 MAT 145
Here is the graph of a function f. Use it to sketch the graph of f ’. Wednesday, February 13, 2019 MAT 145
Sums, differences, exponentials, & products of constants and functions Friday, Sept 21, 2018 MAT 145
Derivatives of Trig Functions Friday, Sept 21, 2018 MAT 145
MAT 145
Friday, Sept 21, 2018 MAT 145
Practice Derivative Rules Friday, Sept 21, 2018 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, Sept 21, 2018 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, Sept 21, 2018
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, Sept 21, 2018 MAT 145
Warm up! . Find the derivatives. Use correct notation! Friday, Sept 21, 2018 MAT 145
Practice Derivative Rules - Answers Friday, Sept 21, 2018 MAT 145
Practice Derivative Rules Friday, Sept 21, 2018 MAT 145
Practice Derivative Rules - Answers Friday, Sept 21, 2018 MAT 145