How do you find the average rate of change of the function #F(x)=x^2-6x+5# over the interval [-2, -2+h]?

Answer 1

#" The Rate="h-10#.

By Defn., the Average rate of Change of a fun. #F : [a,b] rarr RR#, is
#(F(b)-F(a))/(b-a)#.
Hence, the Reqd. Rate#={F(-2+h)-F(-2)}/(-2+h-(-2))#
#={F(h-2)-F(-2)}/h#
#=[(h-2)^2-6(h-2)+5-{(-2)^2-6(-2)+5}]/h#
#=(h^2-4h+4-6h+12+5-4-12-5)/h#
#=(h^2-10h)/h#
#={h(h-10)}/h#
#:." The Rate="h-10#.
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Answer 2

To find the average rate of change of the function (F(x) = x^2 - 6x + 5) over the interval ([-2, -2+h]), you need to calculate the difference in function values over the interval and divide it by the difference in (x) values.

  1. Find (F(-2)) and (F(-2+h)): (F(-2) = (-2)^2 - 6(-2) + 5)
    (F(-2+h) = (-2+h)^2 - 6(-2+h) + 5)

  2. Calculate the difference in function values: (F(-2+h) - F(-2))

  3. Divide the difference in function values by the difference in (x) values: (\frac{F(-2+h) - F(-2)}{(-2+h) - (-2)})

This expression will give you the average rate of change of the function (F(x) = x^2 - 6x + 5) over the interval ([-2, -2+h]).

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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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