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How do you determine the relative minimum and relative maximum values of functions and the intervals on which functions are decreasing or increasing?
You take the derivative of the function. The derivative is another function that tells you the slope of the original function at any point. (If you don't know about derivatives already, you can learn the details on how to calculate in a calculus textbook. Or read the Wikipedia article for a brief introduction.) Once you have the derivative, you solve it for zero (derivative = 0). Any local maximum or minimum either has a derivative of zero, has no defined derivative, or is a border point (on the border of the interval you are considering). Now, as to the intervals where the function increase or decreases: Between any such maximum or minimum points, you take any random point and check whether the derivative is positive or negative. If it is positive, the function is increasing.
How can you tell if a graph sHow is a function?
Test it by the vertical line test. That is, if a vertical line passes through the two points of the graph, this graph is not the graph of a function.
Function equals x to the power of 2 times e to the power of x?
f(x)=(x^2)(e^x) 1. Domain? 2. Symmetry? 3. Intercepts? 4. Asymptotes? 5. Increasing/Decreasing? 6. Relative Extrema? 7. Concave Up/Down? 8. Points Of Inflection? 9. Any Discontinuity? So confused! The e throws me off!
A value is in the domain of a function if there is a what on the graph of the function at that x-value?
points
Can a scatter plot have a linear function?
You can have a line of best fit. It is the line that cuts through the points with the least amount of distance to all the data.
Is the function that cuts through the points 2 3 and -1 6 increasing or decreasing?
Points: (2, 3) and (-1, 6) Slope: -1 therefore it is decreasing
What is the point at which a graph changes directions?
Turning points are the points at which a graph changes direction from increasing o decreasing or decreasing to increasing.
Is a critical point where the graph change its shape but no its increasing or decreasing behavior?
Yes, a critical point can be where the graph changes its shape without changing its increasing or decreasing behavior. This typically occurs at points of inflection, where the concavity of the graph changes, but the function may still be increasing or decreasing. In such cases, the first derivative does not change sign, while the second derivative does, indicating a change in the curvature of the graph rather than a change in the overall trend.
What do the turning points of the graph tell you?
The turning points of a graph indicate where the function changes direction, signaling local maxima and minima. Specifically, a turning point corresponds to a change in the sign of the first derivative, which means the function is either increasing or decreasing before and after that point. Analyzing these points helps identify critical features of the function, such as the overall shape and behavior, which can be useful for optimization and understanding trends.
What must be true about the average rate of change between any two points on the graph of an increasing function?
if a function is increasing, the average change of rate between any two points must be positive.
In a sine wave at what angle or angles is the amplitude increasing at its fastest rate?
The amplitude of a sine wave is increasing at its fastest rate at the maximum points (90°, 270°) and decreasing at its fastest rate at the minimum points (0°, 180°).
Function equals x2ex domain intercepts asymptotes increasing decreasing local extrema concave up concave down points of inflection discontinuous?
f(x)=(x^2)(e^x) 1. Domain? 2. Symmetry? 3. Intercepts? 4. Asymptotes? 5. Increasing/Decreasing? 6. Relative Extrema? 7. Concave Up/Down? 8. Points Of Inflection? 9. Any Discontinuity? So confused! The e throws me off!
When the points on a graph tend to go downward from left to right you say they indicate what?
They mean the graph/function is decreasing.
In which direction do electric field points when the potential is decreasing?
When the potential is decreasing, the electric field points in the direction of decreasing potential.
A sign chart helps you record information about the function's values around its and vertical .?
A sign chart is a visual tool used to analyze the behavior of a function around its critical points, such as zeros and vertical asymptotes. By determining the sign (positive or negative) of the function in different intervals, it helps identify where the function is increasing or decreasing, as well as where it approaches infinity or negative infinity. This information is crucial for understanding the overall shape and behavior of the graph of the function.
What function family has an increasing interval and a decreasing interval?
There are many families of functions or function types that have both increasing and decreasing intervals. One example is the parabolic functions (and functions of even powers), such as f(x)=x^2 or f(x)=x^4. Namely, f(x) = x^n, where n is an element of even natural numbers. If we let f(x) = x^2, then f'(x)=2x, which is < 0 (i.e. f(x) is decreasing) when x<0, and f'(x) > 0 (i.e. f(x) is increasing), when x > 0. Another example are trigonometric functions, such as f(x) = sin(x). Finding the derivative (i.e. f'(x) = cos(x)) and critical points will show this.
What is a trend on a graph?
It is the description of a slope of a line which connects from many points you mark to show a way that your graph data may increase or decrease. If it is decreasing, you have a downwards trend. If it is increasing, you have an upwards trend.
