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
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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