The problem asks us to identify the interval on which the given function is decreasing. The x-coordinates should be integers or values like 0.5, 1.5, etc.

AnalysisFunction AnalysisDecreasing FunctionIntervalGraphing
2025/7/3

1. Problem Description

The problem asks us to identify the interval on which the given function is decreasing. The x-coordinates should be integers or values like 0.5, 1.5, etc.

2. Solution Steps

We need to visually inspect the graph and determine where the function is decreasing (i.e., where the graph is going downwards as we move from left to right).
The function has a local maximum at x=1x = -1. From x=3x = -3 to x=1x = -1, the function increases.
The function decreases from x=1x = -1 to x=1x = 1.
After x=1x = 1, the function increases again.
Therefore, the function is decreasing on the interval (1,1)(-1, 1).

3. Final Answer

-1 < x < 1

Related problems in "Analysis"

The problem asks us to sketch the graphs of two functions: (1) $y = x\sqrt{4-x^2}$ (2) $y = e^{-x} +...

GraphingCalculusDerivativesMaxima and MinimaConcavityInflection PointsDomainSymmetry
2025/7/3

The problem asks to sketch the graph of the function $y = x\sqrt{4 - x^2}$.

CalculusFunction AnalysisDerivativesGraphingDomainCritical PointsLocal Maxima/MinimaOdd Functions
2025/7/3

We are asked to find the sum of the series $\frac{1}{2^2-1} + \frac{1}{4^2-1} + \frac{1}{6^2-1} + \d...

SeriesSummationPartial FractionsTelescoping Series
2025/7/3

The problem asks to evaluate several natural logarithm expressions. The expressions are: 1. $ln(\fra...

LogarithmsNatural LogarithmExponentsLogarithmic Properties
2025/7/3

The problem requires us to analyze a given graph of a function and determine the following: - The in...

Function AnalysisIncreasing and Decreasing IntervalsDomain and Range
2025/7/3

We are given a graph of a function and asked to find the intervals where the function is increasing,...

Function AnalysisIntervalsIncreasing/Decreasing/ConstantDomainRangeGraph Interpretation
2025/7/3

The problem asks us to identify the intervals where the given function is increasing and decreasing,...

Function AnalysisIncreasing and Decreasing IntervalsDomainGraph Interpretation
2025/7/3

The problem asks us to determine the intervals where the given function is increasing and decreasing...

Function AnalysisIncreasing and Decreasing IntervalsDomainGraphing
2025/7/3

The problem asks us to determine the intervals on which the given function is increasing and decreas...

Increasing and Decreasing FunctionsCalculusIntervalsDerivatives (implicitly)
2025/7/3

The problem asks us to draw the tangent line to the curve $y = 3x^5 - 5x^4$ at the inflection point ...

CalculusDerivativesTangent LinesInflection PointsCurve Analysis
2025/6/29