The average rate of change of a function f(x) = x2 between x = 5 and x = 9

Step-by-step explanation:

The average rate of change is given by [g(x_2) - g(x_1)]/(x_2 - x_1). Here, we have x_1 = -2, x_2 = -2 + h, and g(x) = 4/x, so we get:

Average rate of change

= [g(x_2) - g(x_1)]/(x_2 - x_1)

= [4/(-2 + h) - 4/(-2)]/[(-2 + h) - (-2)]

= [4/(-2 + h) + 4/2]/(-2 + h + 2)

= [4/(-2 + h) + 2]/h

To simplfiy this, we combine fractions in the numerator:

[4/(-2 + h) + 2]/h

= [4/(-2 + h) + 2(-2 + h)/(-2 + h)]/h

= {[4 + 2(-2 + h)]/(-2 + h)]}/h

= [(4 - 4 + 2h)/(-2 + h)]/h

= [2h/(-2 + h)]/h

= 2/(-2 + h)

So the average rate of change of g(x) = 4/x between x = -2 and x = -2 + h is 2/(-2 + h).

I hope this helps!

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