# How do you find the average rate of change of #f(x)=-5x+2# from [2,4]?

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To find the average rate of change of ( f(x) = -5x + 2 ) from ( x = 2 ) to ( x = 4 ), you use the formula:

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

where ( a = 2 ) and ( b = 4 ). Substituting these values into the formula:

[ \text{Average Rate of Change} = \frac{f(4) - f(2)}{4 - 2} ]

[ = \frac{(-5 \times 4 + 2) - (-5 \times 2 + 2)}{2} ]

[ = \frac{(-20 + 2) - (-10 + 2)}{2} ]

[ = \frac{-18 - (-8)}{2} ]

[ = \frac{-18 + 8}{2} ]

[ = \frac{-10}{2} ]

[ = -5 ]

So, the average rate of change of ( f(x) = -5x + 2 ) from ( x = 2 ) to ( x = 4 ) is ( -5 ).

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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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