For each table, decide if y’is positive or negative and if y’’ is positive or negative

Slides:



Advertisements
Similar presentations
Application of Derivative in Analyzing the Properties of Functions
Advertisements

Objectives: 1.Be able to determine where a function is concave upward or concave downward with the use of calculus. 2.Be able to apply the second derivative.
Miss Battaglia AP Calculus AB/BC.  Let f be differentiable on an open interval I. The graph of f is concave upward on I if f’ is increasing on the interval.
Concavity and Inflection Points The second derivative will show where a function is concave up or concave down. It is also used to locate inflection points.
Sec 3.4: Concavity and the Second Derivative Test
1 Sec 4.3 Curve Sketching. 2 Curve Sketching Problems Given: A function y = f(x). Objective: To sketch its graph.
First and Second Derivative Test for Relative Extrema
Concavity f is concave up if f’ is increasing on an open interval. f is concave down if f’ is decreasing on an open interval.
Section 5.2 – Applications of the Second Derivative.
Concavity and the Second- Derivative Test. 1. Determine the open intervals on which the graph of the function is concave upward or concave downward (similar.
Increasing / Decreasing Test
AP/Honors Calculus Chapter 4 Applications of Derivatives Chapter 4 Applications of Derivatives.
Definition of the Natural Exponential Function
4.4 Concavity and Inflection Points Wed Oct 21 Do Now Find the 2nd derivative of each function 1) 2)
Using Derivatives to Sketch the Graph of a Function Lesson 4.3.
In the past, one of the important uses of derivatives was as an aid in curve sketching. We usually use a calculator of computer to draw complicated graphs,
SECT 3-8B RELATING GRAPHS Handout: Relating Graphs.
Chapter 16B.5 Graphing Derivatives The derivative is the slope of the original function. The derivative is defined at the end points of a function on.
4.6 Curve Sketching Fri Oct 23 Do Now Find intervals of increase/decrease, local max and mins, intervals of concavity, and inflection points of.
Curve Sketching. Objective To analyze and sketch an accurate graph of a function. To analyze and sketch an accurate graph of a function.
Sketching Functions We are now going to use the concepts in the previous sections to sketch a function, find all max and min ( relative and absolute ),
4.3 – Derivatives and the shapes of curves
4. Concavity and the 2 nd Derivative Test. Concavity If we know that a function has a positive derivative over an interval, we know the graph is increasing,
10/3/2016 Perkins AP Calculus AB Day 5 Section 3.4.
First derivative: is positive Curve is rising. is negative Curve is falling. is zero Possible local maximum or minimum. Second derivative: is positive.
4.3a Increasing and Decreasing Functions And the First Derivative Test
Part (a) In the table, we see that the 1st derivative goes from positive to negative at x=2. Therefore, we know that f(x) has a relative maximum there.
4.3 Using Derivatives for Curve Sketching.
The Second Derivative.
Sketching the Derivative
Second Derivative Test
Lesson 13: Analyzing Other Types of Functions
Concavity of Functions
Relationship between First Derivative, Second Derivative and the Shape of a Graph 3.3.
Lesson 13: Analyzing Other Types of Functions
Concavity and the Second Derivative Test
Concavity and Second Derivative Test
TOPICS ON CHAPTER 4 TEST: 1
3.4 Concavity and the Second Derivative Test
Using Derivatives For Curve Sketching
§4.3. How f   f  affect shape of f
4.3 – Derivatives and the shapes of curves
Section 2.5 The Second Derivative
Second Derivative Test
1 2 Sec 4.3: Concavity and the Second Derivative Test
Application of Derivative in Analyzing the Properties of Functions
Sec 3.4: Concavity and the Second Derivative Test
3.4: Concavity and the Second Derivative Test
MATH 1311 Section 1.3.
5.3 Using Derivatives for Curve Sketching
For each table, decide if y’is positive or negative and if y’’ is positive or negative
Graph of the derived function
4.3 1st & 2nd Derivative Tests
Concavity and the Second Derivative Test
Concavity of a Function
4.3 Connecting f’ and f’’ with the graph of f
Concavity and the Second Derivative Test
1 2 Sec4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH Concavity Test
MATH 1311 Section 1.3.
(4)² 16 3(5) – 2 = 13 3(4) – (1)² 12 – ● (3) – 2 9 – 2 = 7
Derivatives and Graphing
Concavity of a Function
(3, 2) 2 -3 (-4, -3) -2 (5, -2) 1. a) Find: f(3) = ______
1 2 Sec4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH
The First Derivative Test. Using first derivative
4.4 Concavity and the Second Derivative Test
Concavity of a Function
Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH
4.3 Using Derivatives for Curve Sketching.
Relationship between First Derivative, Second Derivative and the Shape of a Graph 3.3.
Presentation transcript:

For each graph, decide if y’is positive or negative and if y’’ is positive or negative

For each table, decide if y’is positive or negative and if y’’ is positive or negative X Y 1 2 3 7 X Y 1 4 2 6 3 7 X Y 1 -1 2 -3 3 -7 X Y 1 -4 2 -6 3 -7

This is a graph of f’(x). Find the following: 1 This is a graph of f’(x). Find the following: 1. Intervals of increase 2. Intervals of decrease 3. Intervals of concave up 4. Intervals of concave down 5. Maxes 6. Mins 7. Points of inflection

Given this graph of the derivative, sketch the graph of the function. Given this graph of the function, sketch the graph of the derivative.