Question

Find the average rate of change of

Answer 1

The average rate of change is 0.14

Solution:

The average rate of change is given as:

$Rate\ of\ change = \frac{f(b) - f(a)}{b-a}$

Given that,

$f(x) = \sqrt{x+6}$

Given interval is [4, 9]

a = 4

b = 9

Find f(b)

$f(9) = \sqrt{9+6}\\\\f(9) = \sqrt{15}\\\\f(9) = 3.872$

Find f(a)

$f(4) = \sqrt{4+6}\\\\f(4) = \sqrt{10}\\\\f(4) = 3.162$

Therefore, average rate of change is given as:

$Rate\ of\ change = \frac{3.872-3.162}{9-4}\\\\Rate\ of\ change = \frac{0.71}{5}\\\\Rate\ of\ change = 0.142 \approx 0.14$

Thus average rate of change is 0.14