The functions f and g are continuous and differentiable with f'(x) = g(x). Selected values of the functions f and g are shown in the table below. What is the average rate of change of f (x) on the interval [0, 8] in simplest form? 8. f 3 1 2 =1 -3 1

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A function is given. g(x) = 5/x ; x=1, x=a (a) Determine the net change between the given values of the variable.     (b) Determine the average rate of change between the given values of the variable.

Select the statement that is false about the difference quotient.   The difference quotient can be represented by f(x+h)−f(x)(x+h)−x or f(x+h)−f(x)h The difference quotient is a more general form of the average rate of change of a function on an interval h units long. The difference quotient describes the general behavior of a function over some interval h units long when the rate of change is not constant. As the value of h gets smaller and smaller, the value of the difference quotient becomes a better and better approximation of the average rate of change of a function f near (x,f(x)). As the value of h gets larger and larger, the value of the difference quotient becomes a better and better approximation of the average rate of change of a function f near (x,f(x)).