The average rate of change of h over the interval is -48 feet per second.
Given,
The height of an object off the ground, h (in feet) t seconds after it is launched into the air is given by
h(t) = −16t2 + 96t, 0 ≤ t ≤ 6.
We need to find the average rate of change of h over the interval [3, 6].
<h3>How do we find the average rate of change of a function over an interval?</h3>
If we have an interval [a, b] and a function f(x).
The rate of change is given by:
= f(b) - f(a) / b - a
We have,
h(t) = −16t² + 96t and [3, 6].
h(6) = -16 x 6² + 96 x 6 = -576 + 576 = 0
h(3) = -16 x 3² + 96 x 3 = -144 + 288 = 144
The average rate of change of h is:
= h(6) - h(3) / 6 - 3
= 0 - 144 / 3
= -144 / 3
= -48
Thus the average rate of change of h over the interval is -48 feet per second.
Learn more about the average rate of change here:
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