g(x)=-4/x; x=-5, x=-5+h Determine the average rate of change of the function between the given values of the variable.
To determine the average rate of change of a function between two given values of the variable, we can use the formula:
Average rate of change = (f(b) - f(a)) / (b - a)
Where "f(b)" represents the value of the function at x = b, "f(a)" represents the value of the function at x = a, and (b - a) represents the difference in the values of x.
In this case, the given values of x are x = -5 and x = -5 + h. Let's find the corresponding values of the function at these points:
f(-5) = -4 / -5 = 4/5
f(-5 + h) = -4 / (-5 + h)
Now we can calculate the average rate of change:
Average rate of change = (f(-5 + h) - f(-5)) / ((-5 + h) - (-5))
Substituting the values we found earlier:
Average rate of change = (-4 / (-5 + h) - 4/5) / (h)
To simplify the expression, we can multiply the numerator and denominator by (-5 + h) to get rid of the fraction in the denominator:
Average rate of change = (-4 - (4/5)(-5 + h)) / h
Simplifying further:
Average rate of change = (-4 + (4/5)(5 - h)) / h
Now we have the average rate of change of the function g(x) = -4/x between x = -5 and x = -5 + h.