Graph Behavior and Derivatives

Graph Behavior and Derivatives

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Hard

Created by

Thomas White

FREE Resource

The video tutorial explores the concepts of derivatives, concavity, and second derivatives. It begins with an introduction to the purpose of the video, followed by an explanation of derivatives and their significance in graph analysis. The discussion then shifts to concavity and the role of second derivatives in determining the rate of change. The video concludes with an analysis of graphs based on these concepts and provides instructions for further engagement.

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14 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the main focus of the video?

Graph plotting techniques

Solving equations

Interpretive analysis of graphs

Chain rule analysis

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What can be said about the slopes of the tangent lines in the top two graphs?

They are always zero

They are always positive

They are always negative

They vary randomly

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does a positive first derivative indicate about a graph?

The graph is constant

The graph is oscillating

The graph is increasing

The graph is decreasing

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the characteristic of the slopes in the bottom two graphs?

Varying between positive and negative

Always negative

Always positive

Always zero

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does a negative first derivative indicate about a graph?

The graph is increasing

The graph is constant

The graph is oscillating

The graph is decreasing

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What do the graphs in the left-hand column have in common?

Both are linear

Both have zero slopes

Both are concave down

Both are concave up

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the second derivative a measure of?

The slope of the graph

The rate of change of the first derivative

The area under the graph

The intercept of the graph

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