# How do you find the average rate of change for the function # f (z) = 5 - 8z^2# on the indicated intervals [-8,3]?

40

to determine the two points' average rate of change.

Here, b = 3 and a = - 8.

The mean rate of variation between (3,-67) and (-8,-507) is

Accordingly, the average of all the tangent line slopes to the f(z) graph between (-8,-507) and (3,-67) is 40.

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To find the average rate of change for the function ( f(z) = 5 - 8z^2 ) on the interval ([-8,3]), use the formula:

[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} ]

where (a) and (b) are the endpoints of the interval.

Plug in the values:

[ f(-8) = 5 - 8(-8)^2 = 5 - 8(64) = 5 - 512 = -507 ]

[ f(3) = 5 - 8(3)^2 = 5 - 8(9) = 5 - 72 = -67 ]

[ \text{Average Rate of Change} = \frac{(-67) - (-507)}{3 - (-8)} = \frac{-67 + 507}{3 + 8} = \frac{440}{11} = 40 ]

Therefore, the average rate of change for the function on the interval ([-8,3]) is (40).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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