# How do you find the average rate of change of #f(x)= 3x^2 - 2x# from 1 to 2?

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As the slope formula of (y2-y1)/(x2-x1) byt instead of y, we have f(x), which is the same thing as the average rate of change, which is the change in y over the change in x.

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To find the average rate of change of ( f(x) = 3x^2 - 2x ) from ( x = 1 ) to ( x = 2 ), you calculate the difference in the function values at the endpoints of the interval and divide by the difference in the input values.

First, evaluate ( f(1) ) and ( f(2) ):

[ f(1) = 3(1)^2 - 2(1) = 3 - 2 = 1 ] [ f(2) = 3(2)^2 - 2(2) = 12 - 4 = 8 ]

Then, calculate the average rate of change using the formula:

[ \text{Average Rate of Change} = \frac{f(2) - f(1)}{2 - 1} ]

[ \text{Average Rate of Change} = \frac{8 - 1}{2 - 1} = \frac{7}{1} = 7 ]

So, the average rate of change of ( f(x) = 3x^2 - 2x ) from 1 to 2 is 7.

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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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