How do you find the average rate of change for the function F(x)=7+ 4/(x+3) on the indicated intervals [-2, -2+h]?

1 Answer
Aug 28, 2015

Average rate of change of F on interval [a,b] is (F(b)-F(a))/(b-a)

Explanation:

So, the average rate of change for the function F(x)=7+ 4/(x+3) on the indicated intervals [-2, -2+h] is:

(F(-2+h)-F(-2))/((-2+h)-(-2))

= ([7+ 4/((-2+h)+3)] -[7+ 4/((-2)+3)])/((-2+h)-(-2)

= (4/(h+1) - 4/1)/h

= ((4-4(1+h))/(1+h))/(h/1)

= (-h)/(h+1) * 1/h

= (-1)/(h+1)
(The last line is equal the preceding lines for x != 0)