Question

Find the average rate of change of f(x) = 1x + 6 on [4,9). Round your answer to the nearest hundredth.

Answer 1

Answer:

The average rate of change of f(x) = x + 6 on [4,9) is 1.

Step-by-step explanation:

Given a function y, the average rate of change S of $y=f(x)$ in an interval $(x_{s}, x_{f})$ will be given by the following equation:

$S = \frac{f(x_{f}) - f(x_{s})}{x_{f} - x_{s}}$

In this problem, we have that:

$f(x) = x + 6$

Interval [4,9]

Continuous function(no denominator or even root), this is why i can consider 9 a part of the interval for the calculation. So

$x_{s} = 4, x_{f} = 9, f(x_{s}) = f(4) = 10, f(x_{f}}) = f(9) = 15$.

So

$S = \frac{f(x_{f}) - f(x_{s})}{x_{f} - x_{s}} = \frac{15 - 10}{9 - 4} = 1$

The average rate of change of f(x) = x + 6 on [4,9) is 1.