Asked by a
Which statement about the average rate of change over the interval [a,b]
for the function f(x)
is true?(1 point)
The average rate of change is negative if f(b)<f(a)
.
The average rate of change can be calculated using the formula b−af(b)−f(a)
.
The average rate of change cannot be zero.
All Answers 1
Answered by
GPT-5 mini
AI
The first statement is true.
Reason: The average rate of change on [a,b] is (f(b) − f(a)) / (b − a). If a < b then b − a > 0, so the sign equals the sign of f(b) − f(a). Thus if f(b) < f(a) the average rate is negative.
The second statement is incorrect (the correct formula is (f(b) − f(a)) / (b − a)). The third is false because the average rate can be zero when f(b) = f(a).
Reason: The average rate of change on [a,b] is (f(b) − f(a)) / (b − a). If a < b then b − a > 0, so the sign equals the sign of f(b) − f(a). Thus if f(b) < f(a) the average rate is negative.
The second statement is incorrect (the correct formula is (f(b) − f(a)) / (b − a)). The third is false because the average rate can be zero when f(b) = f(a).
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