How do you find the average rate of change of the function #f(x)=4 ·x^2 + 2 ·x−4# over the interval [3, 3.17]?
The average rate of change of a function
So, here's where the math comes in:
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To find the average rate of change of the function ( f(x) = 4x^2 + 2x  4 ) over the interval ([3, 3.17]), you calculate the difference in the function values at the endpoints of the interval and divide by the difference in the xvalues.

Evaluate the function at the endpoints of the interval:
 ( f(3) = 4(3)^2 + 2(3)  4 = 36 + 6  4 = 38 )
 ( f(3.17) = 4(3.17)^2 + 2(3.17)  4 = 40.0568 + 6.34  4 = 42.3968 )

Calculate the difference in function values: ( 42.3968  38 = 4.3968 ).

Calculate the difference in xvalues: ( 3.17  3 = 0.17 ).

Divide the difference in function values by the difference in xvalues: ( \frac{4.3968}{0.17} \approx 25.861 ).
So, the average rate of change of the function over the interval ([3, 3.17]) is approximately (25.861).
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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