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Graphing Functions and Critical Points

Graphing Functions and Critical Points

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Practice Problem

Hard

Created by

Jackson Turner

FREE Resource

The video tutorial covers factorization to find roots, calculating first and second derivatives to identify stationary and inflection points, and graphing a quartic function. The instructor explains the process of analyzing the function's features, including horizontal points of inflection and stationary points, and demonstrates how to plot these on a graph. The tutorial emphasizes understanding the shape and behavior of the graph based on the function's derivatives and critical points.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of factorizing the expression to find the roots?

x + 2

x - 4

x + 4

x - 2

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What type of root is associated with the x^3 term?

Double root

Single root

Triple root

Quadruple root

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What are the stationary points identified from the first derivative?

x = 2 and x = 4

x = 1 and x = 3

x = 0 and x = 3

x = 0 and x = 2

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the significance of the leading coefficient in graphing the function?

It determines the color of the graph.

It indicates the number of roots.

It shows the number of stationary points.

It suggests the general shape of the graph.

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What must be verified to confirm a horizontal point of inflection at the origin?

The graph is concave up on both sides.

The graph remains linear.

The graph is concave down on both sides.

The graph changes from concave up to concave down.

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the y-coordinate of the stationary point at x = 3?

-16

0

27

-27

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the y-coordinate of the point of inflection at x = 2?

0

16

-16

-27

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