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## Homework Statement

For the function f(x)=3x^2-1, for what x values is the instantaneous rate of change equal to the average rate of change on the interval [1,3]

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- Thread starter abordel
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For the function f(x)=3x^2-1, for what x values is the instantaneous rate of change equal to the average rate of change on the interval [1,3]

- #2

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1) first find the average rate of change on the interval (1,3)

2) set that number equal to the derivative of the function and solve for x

1) Finding the avg rate of change over the interval 1,3

f(1) = 2

f(3) = 26

so we have (1,2) and (3,26)

the slope give the rate of change so to find the slope between these points

we use the slope formula which gives us 12

2) f `(x) = 3x^2+1

average rate of change = 6x

12 = 6x

x = 2

so when x = 2 in the instantaneous rate of change, it equals the average rate on the

interval [1,3]. notice its between 1 and 3.

- #3

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Just to add you might want to look-up the mean value theorem.

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