How do you find the average rate of change for the function #f(x) = x^2+x+3# on the indicated intervals [1,x]?

Answer 1

x+2

Rate of change would be #(f(x)-f(1))/ (x-1)#
= #((x^2+x+3) -5)/(x-1)#
=#(x^2 +x -2)/(x-1)#
=#((x+2)(x-1))/(x-1)= x+2#
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Answer 2

To find the average rate of change for the function ( f(x) = x^2 + x + 3 ) on the indicated interval ([1,x]), you first need to calculate the value of ( f(x) ) at ( x ), then subtract the value of ( f(1) ) from it. Finally, divide this difference by the change in ( x ), which is ( x - 1 ). This formula gives you the average rate of change over the interval ([1,x]).

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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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