How do you find the average rate of change of # f(x)=x^2-2x# from 1 to 5?

Answer 1

The average rate is #4#.

The average rate of a function #" " f(x)" "#between #" "# #a" " and" "b" "#is defined as: #" "# #" "# #(f(b)-f(a))/(b-a)# #" "# #" "# The average rate of the function #f(x) # between #" "5" " and " "1# #" "# #(f(5)-f(1))/(5-1)# #" "# #" "# Let us evaluate #" "f(5)" and" " f(1)" "# #" "# #f(5) = 5^2 -2(5) = 25 - 10=15# #" "# #f(1) = 1^2 - 2(1) = 1-2 = -1# #" "# #(f(5)-f(1))/(5-1)=(15-(-1))/(5-1)=(15+1)/4 = 16/4 =4# #" "# Hence , #" "# The average rate is #4#.
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Answer 2

To find the average rate of change of ( f(x) = x^2 - 2x ) from ( x = 1 ) to ( x = 5 ), you calculate the change in ( f(x) ) divided by the change in ( x ) over that interval.

First, find the value of ( f(x) ) at the endpoints of the interval:

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

( f(5) = (5)^2 - 2(5) = 25 - 10 = 15 )

Next, calculate the change in ( f(x) ) and ( x ) over the interval:

Change in ( f(x) = 15 - (-1) = 16 )

Change in ( x = 5 - 1 = 4 )

Finally, divide the change in ( f(x) ) by the change in ( x ) to find the average rate of change:

Average rate of change = ( \frac{{16}}{{4}} = 4 )

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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.

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.

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.

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.

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