Question

Given f(x)= x+8

1
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, find the average rate of change of f(x) on the interval [8,8+h]. Your answer will be an expression involving h.

Answer 1

Explanation:

To find the average rate of change of f(x) = x + 8 on the interval [8, 8 + h], we need to calculate the difference in the function values divided by the difference in x-values.

Let's substitute the given interval into the function:

f(8) = 8 + 8 = 16

f(8 + h) = (8 + h) + 8 = h + 16

Now, we can find the average rate of change:

Average Rate of Change = (f(8 + h) - f(8)) / (8 + h - 8)

= [(h + 16) - 16] / h

= h / h

= 1

Therefore, the average rate of change of f(x) on the interval [8, 8 + h] is simply 1.