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flo123
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how do you calculate the rate of change in a graph?? is it just the gradient??
Calculating Rate of Change in Graphs: Is it Just Gradient?
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In summary, the change in Y corresponding to an infinitesimal change in X is the derivative of the function at a specific point.
- #2
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Since your "rate of change" sounds terribly vague,i'll assume that it means "the change in <<y>> corresponding to an infinitesimal change in <<x>>",which means the derivative of the function at a specific point.
Daniel.
Daniel.
- #3
whozum
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dextercioby said:
Usually a premise, whether assumed or not, is followed by a conclusion. You didn't address his question
The rate of change at a point on a graph is the slope or gradient at that given point. For linear graphs of form [itex] y = mx + b [/itex] the gradient is constant throughout the graph, for others calculus is used to find the rate of change.
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HallsofIvy
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whozum said:Usually a premise, whether assumed or not, is followed by a conclusion. You didn't address his question
Yes, he did when he said "which means the derivative of the function at a specific point." "Derivative" is what us Yanks call the "gradient".
- #5
whozum
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HallsofIvy said:
In that case, its a run-on sentence
, and that's why it doesn't make immediate sense.I was taught math in the US and I've only heard gradient when it comes to vector fields. This is the only place I've heard gradient used instead of slope or derivative.
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flo123
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Thanks for the replies, sorry it has caused tension in this debate about my vague question, the derivative of an equation is the gradient simple really... and its a her not a he
plus what other answers other than the change in y and x, could there be on a graph??
plus what other answers other than the change in y and x, could there be on a graph??
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FAQ: Calculating Rate of Change in Graphs: Is it Just Gradient?
What is the purpose of calculating the rate of change in graphs?
The rate of change in graphs is used to determine how much a variable (such as distance, time, or temperature) is changing over a given interval. This information can be useful in analyzing trends, predicting future values, and understanding the relationship between different variables.
How is the rate of change calculated in a graph?
The rate of change is determined by finding the slope of a line connecting two points on the graph. This is done by dividing the change in the y-value (vertical change) by the change in the x-value (horizontal change). This can also be calculated using the formula: (y2-y1)/(x2-x1).
Is the rate of change the same as the gradient in a graph?
Yes, the rate of change and gradient are essentially the same concept. The gradient is the mathematical term for the slope of a line, while the rate of change is a more general term used to describe the change in a variable over time or distance.
Can the rate of change be negative?
Yes, the rate of change can be either positive or negative depending on the direction of the line or the trend in the data. A positive rate of change indicates an increase in the variable over time, while a negative rate of change indicates a decrease.
What are some real-life applications of calculating the rate of change in graphs?
The rate of change is used in many scientific fields, including physics, chemistry, and economics. Some examples of its applications include analyzing the speed of a moving object, determining the rate of chemical reactions, and predicting future stock market trends.