# How do you find the average rate of change of #f(z) = 4 − 3z^2# from [-2,0]?

6

in order to determine the average rate of change between the two usage points.

The mean rate of variation between (0,4) and (-2,-8) is

This indicates that the average slope of all the lines tangent to the f(z) graph is 6.

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To find the average rate of change of ( f(z) = 4 - 3z^2 ) from ( z = -2 ) to ( z = 0 ), you 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. In this case, ( a = -2 ) and ( b = 0 ).

[ f(-2) = 4 - 3(-2)^2 = 4 - 3(4) = 4 - 12 = -8 ] [ f(0) = 4 - 3(0)^2 = 4 ]

Plug these values into the formula:

[ \text{Average rate of change} = \frac{4 - (-8)}{0 - (-2)} = \frac{12}{2} = 6 ]

So, the average rate of change of ( f(z) = 4 - 3z^2 ) from ( z = -2 ) to ( z = 0 ) is ( 6 ).

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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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