Question

A function is given below. Determine the average rate of change of the function between x = 3 and x = 3 + h.

g(x) = -7/x

How do i solve this? I don't seem to be getting the right answer...

Answer 1

find g(3) and g( 3 +h)

average rate of change is

\[\frac{g(3 + h) - g(3)}{ 3+h - 2}\]

substitute and evaluate

Answer 2

What happened to the -7 though?

Answer 3

oops denominator should be 3 + h - 3

Answer 4

\[g(3) = -\frac{7}{3}\]
\[g(3 +h) = -\frac{7}{ 3 + h}\]

Answer 5

so you have average rate of change

\[\frac{-\frac{7}{3 +h} - -\frac{7}{3}}{ 3 +h - 3}\]

Answer 6

Should I get the -7/3+h - -7/3 under the same denominator first or o I start canceling as is?

Answer 7

thats correct... now simplify.... you need a common denominator in the numerator

Answer 8

7h/9+3h for the denominator in the numerator?

Answer 9

or is this wrong?

Answer 10

thats correct, now just divide by h

Answer 11

I get 7/9h+3 as my final answer because I multiplied by the inverse?

Answer 12

thats what I got... well done

Answer 13

The computer said its wrong

Answer 14

I only get one more attempt before it locks me out of a quiz and gives me a 0 on it...

Answer 15

well its my solution.... may be just in the way the answer is written it could be

\[\frac{7}{3(3 + h)}\]

if you're in doubt... use wolframalpha...

Answer 16

Ok, thanks for your help I appreciate it!