How do you find the average rate of change for the function f(z)=5−8z2 on the indicated intervals [-8,3]?

Question

Nico Buck · Accepted Answer

The average rate of change of f(z)over an interval between 2 points (a ,f(a)
and (b ,f(b) is the slope of the secant line connecting the 2 points.
To calculate the average rate of change between the 2 points.

\frac{f (b) - f (a)}{b - a}

here a=-8 and b=3

\Rightarrow f (- 8) = 5 - 8 {(- 8)}^{2} = - 507

and

f (3) = 5 - 8 {(3)}^{2} = - 67

The average rate of change between (-8 ,-507) and (3 ,-67) is

\frac{- 67 - (- 507)}{3 - (- 8)} = \frac{440}{11} = 40

This means that the average of all the slopes of lines tangent to the graph of f(z) between (-8 ,-507) and (3 ,-67) is 40.

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