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A difference quotient is a mathematical expression used to calculate the rate of change of a function at a specific point. It measures the change in the output of a function over a small interval of the input.
A difference quotient is used when we want to find the slope of a curve at a specific point, which helps to determine the rate of change of the function at that point. It is also used in calculus to find derivatives.
To find a difference quotient, you need to first choose two points on the function that are close to each other. Then, calculate the slope of the secant line passing through those two points. Finally, take the limit of this slope as the distance between the two points approaches 0.
Finding a difference quotient allows us to understand the behavior of a function at a particular point. It helps us to determine whether the function is increasing or decreasing at that point, and the rate at which it is changing.
Yes, a difference quotient can be negative if the function is decreasing at the specific point being evaluated. The sign of the difference quotient depends on the direction of the function's change at that point.