# Rate of change

#### flo123

how do you calculate the rate of change in a graph?? is it just the gradient??

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#### dextercioby

Homework Helper
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.

#### whozum

dextercioby said:
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.
Usually a premise, whether assumed or not, is followed by a conclusion. You didn't address his question :rofl:

The rate of change at a point on a graph is the slope or gradient at that given point. For linear graphs of form $y = mx + b$ the gradient is constant throughout the graph, for others calculus is used to find the rate of change.

#### HallsofIvy

Homework Helper
whozum said:
Usually a premise, whether assumed or not, is followed by a conclusion. You didn't address his question :rofl:
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".

#### whozum

HallsofIvy said:
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".
In that case, its a run-on sentence , and thats 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.

#### flo123

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??

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