Compute the average rate of change of the function on the given interval.
f(x) = 16 - 7x on the interval
[-sqrt(5), sqrt(2)]
f(x) = 16 - 7x on the interval
[-sqrt(5), sqrt(2)]
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The average rate of change of f(x) over the interval a ≤ x ≤ b is defined by:
Δf(x)/Δx = [f(b) - f(a)]/(b-a)
For the given function,
Δf(x)/Δx = [(16-7√2) - (16+7√5)]/(√2+√5)
= -7(√2+√5)/(√2+√5)
= -7
Note: It will always be the case the the average rate of change for a linear function anywhere in its domain will be equal to the instantaneous (derivative) rate of change.
Δf(x)/Δx = [f(b) - f(a)]/(b-a)
For the given function,
Δf(x)/Δx = [(16-7√2) - (16+7√5)]/(√2+√5)
= -7(√2+√5)/(√2+√5)
= -7
Note: It will always be the case the the average rate of change for a linear function anywhere in its domain will be equal to the instantaneous (derivative) rate of change.