AP Calculus BC Monday, 14 September 2015 OBJECTIVE TSW (1) define the slope of a curve at a point, and (2) define the derivative. Tests are graded. TODAY’S ASSIGNMENT –Sec. 3.1: pp (17-31 odd) Due on Wednesday/Thursday, 16/17 September, 2015.

Sec. 3.1: Introducing the Derivative

The Tangent Line Problem

Sec. 3.1: Introducing the Derivative The Tangent Line Problem “What is a tangent?”

Sec. 3.1: Introducing the Derivative The Tangent Line Problem

Sec. 3.1: Introducing the Derivative The Tangent Line Problem

Sec. 3.1: Introducing the Derivative The Tangent Line Problem This ratio is also called the difference quotient.

AP Calculus BC Tuesday, 15 September 2015 OBJECTIVE TSW (1) define the slope of a curve at a point, and (2) define the derivative. YESTERDAY’S ASSIGNMENT –Sec. 3.1: pp (17-31 odd) Due Wednesday/Thursday, 16/17 September TODAY’S ASSIGNMENT –Sec. 3.2: pp (5-13 odd, all, 29) Due Friday, 18 September 2015.

Sec. 3.1: Introducing the Derivative Ex: Find the slope of the graph of f (x) = 3x – (4, 7).

Sec. 3.1: Introducing the Derivative Ex: f(x) = x Find the slope of the tangent line at each of the following points: (1, 4), (2, 7), and (–1, 4). Since there are three points at which to find the slope, let’s find the general case first. (Instead of c, we’ll use x. Then, we’ll substitute each of the three x-values to find each slope.

Sec. 3.1: Introducing the Derivative Ex: f(x) = x Find the slope of the tangent line at each of the following points: (1, 4), (2, 7), and (–1, 4).

Sec. 3.1: Introducing the Derivative Ex: f(x) = x Find the slope of the tangent line at each of the following points: (1, 4), (2, 7), and (–1, 4). At (1, 4), m = 2(1) = 2 At (2, 7), m = 2(2) = 4 At (–1, 4), m = 2(–1) = –2

Sec. 3.1: Introducing the Derivative If f (x) is continuous and then the vertical line x = c Is the vertical tangent line to the graph of f. Definition: Vertical Tangent

Sec. 3.1: Introducing the Derivative The Derivative of a Function

Sec. 3.1: Introducing the Derivative

The Derivative of a Function "Derivative" means "slope."

Sec. 3.1: Introducing the Derivative The Derivative of a Function

Sec. 3.1: Introducing the Derivative Ex: Find the derivative of f(x) = x 3 + 2x.

Sec. 3.1: Introducing the Derivative Ex: Find f'(x) for Then find the slope of the graph of f at the points (1, 1) and (4, 2). Discuss the behavior of f at (0, 0).

AP Calculus BC Thursday, 17 September 2015 OBJECTIVE: TSW use basic differentiation rules to find derivatives, slopes of tangent lines, equations of tangent lines, and rates of change. ASSIGNMENT DUE BY END OF PERIOD –Sec. 3.1: pp (17-31 odd)  wire basket (I will address some “issues” first) TUESDAY’S ASSIGNMENT –Sec. 3.2: pp (5-13 odd, all, 29) Due tomorrow, Friday, 18 September TODAY’S ASSIGNMENT –REGISTER YOUR ACCOUNT!!! –Sec. 3.3: pp (7-17 odd, all omit 21, 35, 36) Due Monday, 21 September QUIZ: Sec. 3.1 – 3.3 is tomorrow, Friday, 18 September –No calculator!

Sec. 3.1: Introducing the Derivative Ex: Find f'(x) for Then find the slope of the graph of f at the points (1, 1) and (4, 2). Discuss the behavior of f at (0, 0). At (0, 0), f '(0) = ∞,  f has a vertical tangent at x = 0.

Sec. 3.1: Introducing the Derivative Ex: Find the derivative with respect to t for the function y = 2 / t.