Question

Find the average rate of change of the function from to f(x)= square root of x from x1=4 to x2=121

Answer 1

$f(x) = \sqrt x$

$x_1=4, x_2 = 121$

Main formula: $A(x) = \frac{\Delta y}{ \Delta x} = \frac{f(x+h) -f(x)}{h}$

Find $f(x+h)$ :

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

Find $h$:

$h = x_2 - x_1 = 121 - 4 = 117$

Find the average rate of change by using our main formula:

$A(x) = \frac{f(x+h) - f(x)}{h} = \frac{\sqrt{4+117} - \sqrt{4}}{117} = \frac{11 - 2}{117} = \frac{9}{117} = \frac{1}{3}$

The answer is: $\bold{\frac{1}{3}}$