# What is the average rate of change of the function #f(z) = 2-5(z^2)# on the interval [-7,2]?

(Yes, that is the same as the slope of the line through the endpoints on the graph.)

So, for this question the answer is

Do the arithmetic.

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To find the average rate of change of the function ( f(z) = 2 - 5z^2 ) on the interval ([-7,2]), we use the formula:

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

where ( f(b) ) is the value of the function at the upper limit of the interval (( b )), ( f(a) ) is the value of the function at the lower limit of the interval (( a )), and ( b - a ) is the length of the interval.

Substituting the values into the formula:

[ f(-7) = 2 - 5(-7)^2 = 2 - 5(49) = 2 - 245 = -243 ] [ f(2) = 2 - 5(2)^2 = 2 - 5(4) = 2 - 20 = -18 ]

So, the average rate of change of ( f(z) ) on the interval ([-7,2]) is:

[ \frac{-18 - (-243)}{2 - (-7)} = \frac{-18 + 243}{2 + 7} = \frac{225}{9} = 25 ]

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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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