When are you closest to the candy?

Slides:

Advertisements

Similar presentations

Is the shape below a function? Explain. Find the domain and range.

Advertisements

Equations of Tangent Lines

Modeling and Optimization

Support Vector Machines Exercise solutions Ata Kaban The University of Birmingham.

Unit 7 - Lesson 2 Rate of Change – Part 1 15 Learning Goals: I can determine the rate of change of a linear relation using a graph. I can determine what.

Math – Getting Information from the Graph of a Function 1.

September 17, 2012 Analyzing Graphs of Functions

Section 5.1 – Increasing and Decreasing Functions The First Derivative Test (Max/Min) and its documentation 5.2.

September 18, 2012 Analyzing Graphs of Functions Warm-up: Talk to your group about the Distance Formula worksheet given last week. Make sure you understand.

Logarithms Year 11 Maths Extension. Logarithms Examples.

MAT 1221 Survey of Calculus Section 4.3 Derivatives of Exponential Functions

Graphs with restricted(forbidden) regions!. From this information, we can complete the sketch Note that the graph is symmetrical about the y-axis, so.

Constant velocity Monday, September 14, Monday, 9/14 Unit 1: Linear Motion  Find out what your elbow partner said would stop Messi. Write your.

Chapter 9.1 Notes. Quadratic Function – An equation of the form ax 2 + bx + c, where a is not equal to 0. Parabola – The graph of a quadratic function.

Using Derivatives for Curve Sketching

Optimization Problems

What is acceleration? – Probably heard it mean: “the process of speeding up” – More specifically: the rate at which velocity changes. Remember that velocity.

Motion Graph (time and distance)  You are to mark a starting line.  You are going to walk at a normal pace.  Your partner will mark with tape the distance.

Task 2: The Design A roller coaster can be based on mathematical functions, but they are more likely to be made up of pieces, each of which is a different.

Distance on a coordinate plane. a b c e f g d h Alternate Interior angles Alternate exterior angles corresponding angles supplementary angles.

First derivative: is positive Curve is rising. is negative Curve is falling. is zero Possible local maximum or minimum. Second derivative: is positive.

The Product and Quotient Rules

AIM: Why is knowing calibration important

Roller Coaster Physics

Jeopardy Speed Velocity Acceleration Graphing $100 $100 $100 $100 $100

Trigonometric Functions Review

Warm Up Solve by factoring. x2 + 10x + 25 x2 – 16x + 64 x2 + 18x + 81.

Investigating Energy Day 2.

Slope of a Line (6.1).

The Second Derivative.

قطار التعرج مجلس أبوظبي للتعليم منطقة العين التعليمية

Quick Question: The Top Thrill Dragster Coaster is the 2nd

Midterm Review Answers #23-43

TOPICS ON CHAPTER 4 TEST: 1

Grade 6 Geometry and Measures Upper and Lower Bounds 2.

Graph 2 Graph 4 Graph 3 Graph 1

Using Derivatives For Curve Sketching

Section 3.6 Calculus AP/Dual, Revised ©2017

Second Derivative Test

ماذا نعني بأن الطاقة كمية محفوظة؟!

Without using a calculator!

A graphing calculator is required for some problems or parts of problems 2000.

Optimization Rizzi – Calc BC.

8-2 Characteristics of Quadratic Functions Warm Up Lesson Presentation

Critical Points and Extrema

5.2 Section 5.1 – Increasing and Decreasing Functions

Section 7.2 Day 1 Disk method

LESSON 10–8 Equations of Circles.

LESSON 10–8 Equations of Circles.

4.3 Connecting f’ and f’’ with the graph of f

1.5: Velocity-time graphs

Bellwork: 2/6/18 2) Factor: x2-x-6 (x-6) (2x+5)

Speed, Distance, Time Calculations

Distance And Midpoint Section 1-3 Spi.2.1.E Jim Smith JCHS.

“Yesterday was a good day……” Journey 1979

Distance And Midpoint Section 1-5.

Circumference & Composite Figures

Speed, Distance, Time Calculations

Motion Section 3 Acceleration

Notebook Response – Changes in Motion Objective: We will calculate the average speed of a marble using a roller coaster model. Create a line graph that.

Maximum and Minimum Points

Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH

Five-Minute Check (over Lesson 9–6) Mathematical Practices Then/Now

Acceleration Chapter 9.3 Page 350.

COMPASS Practice Test 16.

4.3 Using Derivatives for Curve Sketching.

Presentation transcript:

When are you closest to the candy? An optimization roller coaster odyssey

Problem: You are riding a roller coaster. You need to grab a piece of candy on your way by. Calculate when you will be closest to the candy. Roller Coaster Video

Where is the roller coaster closest to the candy Where is the roller coaster closest to the candy? How long of a stick will you need to grab the candy? Things to remember: Distance formula (we derived this yesterday) Use your calculator You will come up with more than one answer. The derivative is 0 in 5 places. Remember you need to figure out which is the minimum Link to DESMOS for this question

What does the distance graph look like? Lots of mins and maxes

Distance and Derivative How do the mins and maxes correspond to the derivative graph?