Math Problem Statement

Use the graph of g in the figure to do the following. a. Find the values of x in left parenthesis negative 4 comma 4 right parenthesis at which g is not continuous. b. Find the values of x in left parenthesis negative 4 comma 4 right parenthesis at which g is not differentiable. c. Sketch a graph of g prime. -4 -2 2 4 6 8 10 -2 2 4 6 8 10 x y

A coordinate system has a horizontal x-axis labeled from negative 5 to 10 in increments of 1 and a vertical y-axis labeled from negative 2 to 10 in increments of 1. A curve consists of two pieces. The first piece is a downward opening parabola that starts at (negative 4, 4), rises to a vertex at (negative 2, 6), and then falls ending at (0, 4). The second piece is another downward opening parabola that starts at (0, 4), rises to a vertex at (2, 5), and then falls ending at (4, 4). There is a hole in the graph at (negative 2, 6). . . . Question content area right Part 1 a. In the interval left parenthesis negative 4 comma 4 right parenthesis​, g is not continuous at xequals    negative 2. ​(Use a comma to separate answers as​ needed.) Part 2 b. In the interval left parenthesis negative 4 comma 4 right parenthesis​, g is not differentiable at xequals    negative 2 comma 0. ​(Use a comma to separate answers as​ needed.) Part 3 c. Choose the correct graph. A. -8 8 x y

A coordinate system has a horizontal x-axis labeled from negative 8 to 8 in increments of 2 and an unlabeled vertical y-axis. A graph consists of two branches. The first branch is a line segment that extends from an endpoint above the x-axis at x equals negative 4 to an open endpoint below the x-axis at x equals 0. The second branch is a line segment that extends from an open endpoint above the x-axis at x equals 0 to an endpoint below the x-axis at x equals 4. There is a hole in the graph on the x-axis at x equals negative 2. B. -8 8 x y

A coordinate system has a horizontal x-axis labeled from negative 8 to 8 in increments of 2 and an unlabeled vertical y-axis. A graph consists of two branches. The first branch is a line segment that extends from an endpoint below the x-axis at x equals negative 4 to an open endpoint above the x-axis at x equals 0. The second branch is a line segment that extends from an open endpoint that is below the open endpoint of the first branch at x equals 0 and above the x dash axis. The branch extends to an endpoint below the x-axis at x equals 4. There is a hole in the graph on the x-axis at x equals negative 2. C. -8 8 x y

A coordinate system has a horizontal x-axis labeled from negative 8 to 8 in increments of 2 and an unlabeled vertical y-axis. A graph consists of two branches. The first branch is a line segment that extends from an endpoint above the x-axis at x equals negative 4 to an open endpoint below the x-axis at x equals 0. The second branch is a line segment that extends from an open endpoint that is above the open endpoint of the first branch at x equals 0 and below the x dash axis. The branch extends to an endpoint above the x-axis at x equals 4. There is a hole in the graph on the x-axis at x equals negative 2. D. -8 8 x y

Solution

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Continuity
Differentiability
Graphical Analysis
Derivatives

Formulas

Conditions for continuity
Conditions for differentiability
Derivative of a quadratic function

Theorems

Intermediate Value Theorem
Mean Value Theorem
Definition of Continuity and Differentiability

Suitable Grade Level

Grades 10-12