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Apost8
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This isn't a homework question, but I'm wondering if the following two equations can always be used interchangeably (thanks in advance):
f(x)-f(c)/(x-c)
and
f(a+h)-f(a)/h
f(x)-f(c)/(x-c)
and
f(a+h)-f(a)/h
Data said:yes, it's just substituting x for a+h and c for a, so then h = x-c.
arildno said:Do not double post!
A difference quotient is a mathematical expression used to find the slope of a curve at a specific point. It is essentially the average rate of change between two points on a curve.
To calculate a difference quotient, you must first choose two points on a curve: (x, f(x)) and (x+h, f(x+h)). The difference quotient is then found by taking the limit as h approaches 0 of (f(x+h) - f(x)) / h.
Yes, the difference quotient can be used to find the slope of any curve, as long as the curve is continuous and differentiable at the given point.
Interchanging difference quotients means to switch the positions of the two points used in the calculation. This is possible because the order of the points does not affect the final result.
Understanding difference quotients and their interchangeability is important because they are fundamental concepts in calculus and are used to find the derivative of a function. This is essential in many fields of science and engineering, such as physics, economics, and engineering.