A function is given. Determine the average rate of change of the function between the given values of the variable.

Question

g(x) =  2

x + 6

x = 0,  x = h

*That is a fraction above (2/x+6)... not two different questions

Answer 1

f(x) = 2/(x+6)

f(h) = 2/(h+6)

f(0) = 2/6 = 1/3

f(h) - f(0) = 2/(h+6) - 1/3

= [2*3 - (h+6)] / 3(h+6)

= [6 - h - 6]/ 3(h+6)

= -h / 3(h+6)

dividing by h:

-1/ 3(h+6)