Question

What is the simplified form of the difference quotient?

1) f(x) = (f(x + h) - f(x))/h
2) f(x) = (f(x) - f(x + h))/h
3) f(x) = (f(x + h) - f(x))/x
4) f(x) = (f(x) - f(x + h))/x

Answer 1

The simplified form of the difference quotient is f(x) = (f(x + h) - f(x))/h, which is important in calculus for finding the derivative.

Step-by-step explanation:

The simplified form of the difference quotient is given by the expression f(x) = (f(x + h) - f(x))/h. This is the standard form used in calculus to represent the average rate of change of the function f over the interval from x to x + h. As h approaches zero, the difference quotient often leads to the derivative of the function at x, which represents the instantaneous rate of change of the function at that point.