Answer :
The average rate of change of f(x) = -11√x + 14 over the interval [-10, -9]. is 0.7
What is the average rate of change?
The average Rate of Change of the function f(x) can be calculated as;
[tex]f(x) = \dfrac{f(b) - f(a)}{b-a}[/tex]
We have been given the function as; f(x) = -11√x + 14 over the interval [-10, -9].
i.e. a = -10 and b = -9
Therefore, f(x) = -11√x + 14
f(-9) = -11√(-9) + 14
f(-9) = -33 + 14
f(-9) = -19
Also, f(-10) = -11√(-10) + 14
f(-10) = - 34.7 + 14
f(-10) = 20.7
Now, substitute the values;
[tex]f(x) = \dfrac{f(b) - f(a)}{b-a}\\f(x) = \dfrac{f(-9) - f(-10)}{-9+ 10}\\f(x) = \dfrac{-19-20.7}{1}\\f(x) = 0.7[/tex]
Hence, the average rate of change of f(x) = -11√x + 14 over the interval [-10, -9]. is 0.7
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