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Find the average rate of change of the function from x = 1 to x = 2.F (x) = - 14/ x squared (x2)

Find The Average Rate Of Change Of The Function From X 1 To X 2F X 14 X Squared X2 class=

Sagot :

Given the function f(x) defined as:

[tex]f(x)=-\frac{14}{x^2}[/tex]

In general, to find the average rate of change of the function from x = a and x = b (a < b), we use the formula:

[tex]Av=\frac{f(b)-f(a)}{b-a}[/tex]

For this problem, a = 1 and b = 2. Then, we calculate f(1) and f(2) first:

[tex]\begin{gathered} f(1)=-\frac{14}{1^2}=-14 \\ f(2)=-\frac{14}{2^2}=-3.5 \end{gathered}[/tex]

Finally, using the formula for the average rate of change:

[tex]Av=\frac{-3.5-(-14)}{2-1}=\frac{-3.5+14}{1}=10.5[/tex]

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