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2.1 Tangent Line Problem
Tangent Line Problem The tangent line can be found by finding the slope of the secant line through the point of tangency and a point on the curve Point A is the point of tangency
Tangent Line Problem How to find slope of a curve at a point? xx + Δx Secant Line Tangent Line
xx + Δx Setting up a limit! Slope of the Tangent Line
1.) Find slope of the secant line x x + Δx Secant Line
xx + Δx Called the difference quotient Conclusion:
For a function f(x) the average rate of change along the function is given by: Which is called the derivative of f Definition of the Derivative
Notation of the Derivative The derivative of a function at x is given by: **Provided the limit exists Notation:
2.) Find the slope of the tangent line to the curve at (2,6) First, find the Slope at any point
Terminology Differentiation (Differentiate) – the process of finding the derivative Differentiable – when a functions derivative exists at x
When Derivatives Fail 1.Cusp or sharp point: cusp
When Derivatives Fail 2.Vertical asymptotes: 3.When one sided limits fail
When Derivatives Fail 4.Removable discontinuity
When Derivatives Fail 5. Corners or vertical tangents
3.) Differentiate (if possible)
4.) Differentiate (if possible)
5.) Differentiateif possible
6.) Find the derivative of
HOMEWORK Page 104 # 5 – 21 (odd), 61 and 62, 83-88 (all). Find where f(x) is not differentiable and state the type of discontinuity
DERIVATIVE OF A FUNCTION 1.5. DEFINITION OF A DERIVATIVE OTHER FORMS: OPERATOR:,,,
Today in Calculus Go over homework Derivatives by limit definition Power rule and constant rules for derivatives Homework.
D EFINITION OF THE D ERIVATIVE Derivatives Review- 1.
SECTION 3.1 The Derivative and the Tangent Line Problem.
Derivatives Test Review Calculus. What is the limit equation used to calculate the derivative of a function?
1 The Derivative and the Tangent Line Problem Section 2.1.
2.1 The Derivative and The Tangent Line Problem
THE DERIVATIVE AND THE TANGENT LINE PROBLEM
Sec 3.1: Tangents and the Derivative at a Point
1.4 – Differentiation Using Limits of Difference Quotients
Lesson 3.2 Differentiability AP Calculus Mrs. Mongold.
Differentiable vs. Continuous The process of finding the derivative of a function is called Differentiation. A function is called Differentiable at x if.
Limits Pre-Calculus Calculus.
2.1 The Derivative and the Tangent Line Problem Objectives: -Students will find the slope of the tangent line to a curve at a point -Students will use.
1.5 Cusps and Corners When we determine the derivative of a function, we are differentiating the function. For functions that are “differentiable” for.
Sec 3.2: The Derivative as a Function If ƒ’(a) exists, we say that ƒ is differentiable at a. (has a derivative at a) DEFINITION.
Implicit Differentiation Objective: To find derivatives of functions that we cannot solve for y.
AP Calculus Review
1 Discuss with your group. 2.1 Limit definition of the Derivative and Differentiability 2015 Devil’s Tower, Wyoming Greg Kelly, Hanford High School, Richland,
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