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How do you find the average rate of change of #f(x)=10x^3+10# over the interval [1,3]?

Answer 1

Evelyn Agard

The average rate of change can be found through finding #(f(3)-f(1))/(3-1)#.

#(f(3)-f(1))/(3-1)=((10(3^3)+10)-(10(1^3)+10))/2=(270-10)/2=130#

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Answer 2

Luke Alvarez

To find the average rate of change of (f(x) = 10x^3 + 10) over the interval ([1, 3]), you can use the formula:

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

where (a) and (b) are the endpoints of the interval.

In this case, (a = 1) and (b = 3). Substituting these values into the formula and evaluating (f(1)) and (f(3)), we get:

[ \text{Average Rate of Change} = \frac{f(3) - f(1)}{3 - 1} ]

[ f(1) = 10(1)^3 + 10 = 10 + 10 = 20 ]

[ f(3) = 10(3)^3 + 10 = 10(27) + 10 = 270 + 10 = 280 ]

[ \text{Average Rate of Change} = \frac{280 - 20}{3 - 1} = \frac{260}{2} = 130 ]

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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.