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How do you find the average rate of change of #y=x^2-x+1# over [0,3]?

Answer 1

Paisley Johnson

The average rate of change of function #f# over interval #[a,b]# is #(f(b)-f(a))/(b-a)#

For #f(x) = x^2-x+1# over #[0,3]#, the average rate of change is

#(f(b)-f(a))/(b-a) = (f(3)-f(0))/(3-0)#

# = (7-1)/3 = 6/3 = 2#

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Answer 2

Evelyn Agard

To find the average rate of change of ( y = x^2 - x + 1 ) over the interval [0,3], you first need to calculate the values of the function at the endpoints of the interval, which are ( x = 0 ) and ( x = 3 ). Then, find the difference in the values of the function at these endpoints, and divide this difference by the difference in the corresponding values of ( x ), which is ( 3 - 0 = 3 ). This gives you the average rate of change of the function over the interval [0,3].

Substitute ( x = 0 ) and ( x = 3 ) into the function: ( y(0) = (0)^2 - 0 + 1 = 1 ) ( y(3) = (3)^2 - 3 + 1 = 7 )

The difference in the values of the function at the endpoints is: ( 7 - 1 = 6 )

The difference in the values of ( x ) at the endpoints is: ( 3 - 0 = 3 )

Therefore, the average rate of change of the function over the interval [0,3] is: ( \frac{6}{3} = 2 )

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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.