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Mathematics
What is the average rate of change of g ( x ) = 2 x + 3 g(x)=(2)/(x+3) over the interval 1 x 3 1 <= x <= 3 ?
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The average rate of change of g ( x ) = 2 x + 3 g(x)=(2)/(x+3) over the interval 1 x 3 1 <= x <= 3 is given by the formula:
g ( 3 ) g ( 1 ) 3 1 (g(3)-g(1))/(3-1)
We need to compute g ( 3 ) g(3) and g ( 1 ) g(1):
g ( 3 ) = 2 3 + 3 = 1 3 g(3)=(2)/(3+3)=(1)/(3)
g ( 1 ) = 2 1 + 3 = 1 2 g(1)=(2)/(1+3)=(1)/(2)
Substituting these values, we get:
g ( 3 ) g ( 1 ) 3 1 = 1 3 1 2 2 = 1 6 (g(3)-g(1))/(3-1)=((1)/(3)-(1)/(2))/(2)=(-1)/(6)
Therefore, the average rate of change of g ( x ) = 2 x + 3 g(x)=(2)/(x+3) over the interval 1 x 3 1 <= x <= 3 is 1 6 (-1)/(6).
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