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DERIVATIVE OF A FUNCTION 1.5
DEFINITION OF A DERIVATIVE OTHER FORMS: OPERATOR:,,,
DERIVATIVES ****THE DERIVATIVE IS A FUNCTION. IF YOU PLUG IN AN X VALUE, THE DERIVATIVE WILL TELL YOU THE SLOPE OF THE TANGENT LINE AT THAT X VALUE.
EXAMPLE 1 A)FIND THE DERIVATIVE: B)FIND THE SLOPE OF THE TANGENT LINE AT X=2
EXAMPLE 2 FIND DY/DX:
DIFFERENTIABILITY A FUNCTION IS DIFFERENTIABLE EVERYWHERE THAT THE DERIVATIVE EXISTS.
WHAT IT LOOKS LIKE TO NOT BE DIFFERENTIABLE AT A CORNER AT A CUSP AT A VERTICAL TANGENT AT A DISCONTINUITY
ONE SIDED DERIVATIVES SHOW THAT THE FOLLOWING FUNCTION IS NOT DIFFERENTIABLE AT X = 0
APPROXIMATE THE VALUE OF THE DERIVATIVE F(X) F’(1) F’(3) F’(2) F’(-1)
SKETCHING THE GRAPH GIVEN F(X) GRAPH F’(X)
HOMEWORK PG 144 #25, 26 ANSWER THE QUESTION AND APPROXIMATE THE VALUE OF F’(X1), F’(X7) PG 156 #1-31 ODD
Differentiability and Piecewise Functions. What are the three things that make a function not differentiable ? Not continuous at the point Vertical tangent.
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Drill Tell whether the limit could be used to define f’(a).
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Chapter 2 Section 2 The Derivative!. Definition The derivative of a function f(x) at x = a is defined as f’(a) = lim f(a+h) – f(a) h->0 h Given that a.
AP Calculus AB/BC 3.2 Differentiability, p. 109 Day 1.
2.1 The Derivative and The Tangent Line Problem The Definition of a Derivative.
Homework Quiz Page 105 Exercises 2 & 8 Show work!.
THE DERIVATIVE AND THE TANGENT LINE PROBLEM Section 2.1.
The Derivative and the Tangent Line Problem. Local Linearity.
1. Consider f(x) = x 2 What is the slope of the tangent at a=0?
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Lesson 2-9 Derivatives as Functions. Objectives Understand the difference between differentiability and continuity.
GOAL: USE DEFINITION OF DERIVATIVE TO FIND SLOPE, RATE OF CHANGE, INSTANTANEOUS VELOCITY AT A POINT. 3.1 Definition of Derivative.
Suppose that functions f and g and their derivatives have the following values at x = 2 and x = –4 1/3–3 5 Evaluate the derivatives with.
2.1 The Derivative and the Tangent Line Problem.
Section 3.2 Differentiability. Ways a function might not be differentiable. 1. a corner Often occurs with absolute value functions.
Section 3.2 Calculus Fall, Definition of Derivative We call this derivative of a function f. We use notation f’(x) (f prime of x)
Warm Up 1)Sketch the graph of y = ln x a)What is the domain and range? b)Determine the concavity of the graph. c)Determine the intervals where the graph.
Derivatives - Equation of the Tangent Line Now that we can find the slope of the tangent line of a function at a given point, we need to find the equation.
Aim: How do we take second derivatives implicitly? Do Now: Find the slope or equation of the tangent line: 1)3x² - 4y² + y = 9 at (2,1) 2)2x – 5y² = -x.
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3.1 Derivatives of a Function, p. 98 AP Calculus AB/BC.
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Derivatives of Logarithmic Functions Objective: Obtain derivative formulas for logs.
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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,
3.1 Derivative of a Function What youll learn Definition of a derivative Notation Relationships between the graphs of f and f Graphing the derivative from.
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