Difference Quotient Formula
f(x+h)-f(x)/h
The difference quotient formula is a mathematical expression used to calculate the slope of a curve or a line at two points. It is commonly used in calculus to analyze a function’s rate of change.
The general formula for the difference quotient is:
(f(x + h) – f(x)) / h
where f(x) is the original function, h is the difference between two x-values, and (x+h) and x represent two points on the function.
To use this formula, you need to find two points on the function, which could be any two x-values or a point and a nearby point. Once you have identified these points, substitute their values into the formula and simplify the equation.
For example, suppose you have a function f(x) = x^2 and you want to find the slope of the curve at x=2. Using the difference quotient formula, you would have:
(f(x + h) – f(x)) / h
= ((2 + h)^2 – 2^2) / h
= (4 + 4h + h^2 – 4) / h
= (4h + h^2) / h
= 4 + h
Thus, the slope of the curve at x=2 is 4.
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