Math Problem Statement

The function graphed above is decreasing on the interval

< x <

The inflection point is at x =

The function graphed above is decreasing on the interval < x < The inflection point is at x =

Solution

The graph shows a function with critical points, regions of increase and decrease, and a clear inflection point. Let me address your two questions based on the graph:

  1. Intervals of Decrease: The function is decreasing where the slope of the graph is negative. From observation:

    • The function decreases from around x=4x = -4 to x=2x = -2.
    • It also decreases from x=0x = 0 to approximately x=1x = 1.

    Therefore, the function is decreasing on the intervals: (4,2)(0,1)(-4, -2) \cup (0, 1)

  2. **Inflection Point:

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Math Problem Analysis

Mathematical Concepts

Calculus
Functions
Inflection Points
Intervals of Increase and Decrease

Formulas

-

Theorems

Critical Points Theorem
Inflection Point Theorem

Suitable Grade Level

Grades 10-12