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How do you find the average rate of change of #f(x) = 17-x^2# over the interval [1, 5]?

Answer 1

Ezekiel Alexander

Average rate of change is -6

Rate of change at any point is #f^'(x) = -2x#

At #x=1 -> f^1 =-2#

At #x=5->f^'=-10#

Throughout this period, the mean rate of change is:

#(-2-10)/2 = -6#

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Answer 2

Christopher Agresta

To find the average rate of change of ( f(x) = 17 - x^2 ) over the interval ([1, 5]), you first find the values of the function at the endpoints of the interval ((x = 1) and (x = 5)). Then, you calculate the difference in the function values and divide by the difference in the corresponding x-values.

( f(1) = 17 - 1^2 = 16 )

( f(5) = 17 - 5^2 = -8 )

Average rate of change = ( \frac{f(5) - f(1)}{5 - 1} = \frac{-8 - 16}{5 - 1} = \frac{-24}{4} = -6 )

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Answer from HIX Tutor

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.