Answered

What is the average rate of change of g(x)=\dfrac{2}{x+3}g(x)= x+3 2 ​ g, left parenthesis, x, right parenthesis, equals, start fraction, 2, divided by, x, plus, 3, end fraction over the interval 1\le x \le31≤x≤31, is less than or equal to, x, is less than or equal to, 3?

Answer :

lublana

Answer:

[tex]-\frac{1}{12}[/tex]

Explanation:

We are given that

[tex]g(x)=\frac{2}{x+3}[/tex]

Interval=[1,3]

We h of have to find the average rate of change of g(x).

Let a=1 and b=3

[tex]g(1)=\frac{2}{1+3}=\frac{2}{4}=\frac{1}{2}[/tex]

[tex]g(3)=\frac{2}{3+3}=\frac{2}{6}=\frac{1}{3}[/tex]

Mean value theorem

Average rate of change of g(x)=[tex]\frac{g(b)-g(a)}{b-a}[/tex]

Using mean value theorem

Average rate of change of g(x)=[tex]\frac{\frac{1}{3}-\frac{1}{2}}{3-1}=-\frac{1}{2\times 6}[/tex]

Average rate of change of g(x)=[tex]-\frac{1}{12}[/tex]

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