Which statement about the average rate of change over the interval [a,b]

Question

for the function f(x)
is true?(1 point)
Responses

The average rate of change cannot be zero.
The average rate of change cannot be zero.

The average rate of change is negative if f(b)<f(a)
.
The average rate of change is negative if f left parenthesis b right parenthesis less than f left parenthesis a right parenthesis .

The average rate of change can be calculated using the formula b−af(b)−f(a)
.
The average rate of change can be calculated using the formula Start Fraction b minus a over f left parenthesis b right parenthesis minus f left parenthesis a right parenthesis End Fraction .

The average rate of change can be calculated using the formula f(b)−f(a)a−b
.

Answer 1

The correct statement from the provided options about the average rate of change over the interval \([a,b]\) for the function \(f(x)\) is:

The average rate of change can be calculated using the formula \(\frac{f(b) - f(a)}{b - a}\).

This formula correctly represents the average rate of change of the function \(f(x)\) over the interval \([a, b]\). It measures how much the function value changes (the difference \(f(b) - f(a)\)) relative to the change in the input values (the difference \(b - a\)).

The other statements contain inaccuracies or repetitions and are not correct representations of the average rate of change.