Classroom Resource

Using the First and Second Derivative Tests

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

This informational material will explain how to describe the relationship between two variables as either concavity or inflection using functions and graphical representations:

- When the sign is negative, the curve is concave down.
- When the sign is positive, the curve is concave up.

There is a corresponding video available. Practice questions with a PDF answer key are provided.

Content Standards

Mathematics (2019) Grade(s): 09-12 - Mathematical Modeling

MA19.MM.15
Use regression with statistical graphing technology to determine an equation that best fits a set of bivariate data, including nonlinear patterns.

Unpacked Content

Vocabulary

Regression Equation
"Best Fit"
Bivariate Data
Linear Pattern
Non-linear pattern
Scatter Plot
Quantitative Variable
Extrema
Inflection

Knowledge

Students know:

how to plot points using graphing technology.
how to find a regression equation using graphing technology.
how to use a regression equation to make a prediction.

Skills

Students are able to:

plot points.
Distinguish between linear and nonlinear functions.
Use graphing technology.

Understanding

Students understand that:

Regression equations can be used to model data.
Graphing technology helps us find regression equations.
The regression equation can be used to make a prediction.

Interdisciplinary Connection(s)

Link to Resource

https://www.ck12.org/c/calculus/concavity-and-inflection/lesson/Using-the-First…

Content Type / Source

Resource Provider

Other

Resource Provider other

CK-12

Accessibility

License

License Type

CUSTOM

Custom License Type (URL)

https://www.ck12info.org/terms-of-use/

Approved Date

2022-12-04

Curated by

habradley

Design by Adaptive Theme

Learning Resource Type