SOLUTION: If f(x)= -2/x+3, what would be the simplest form of f(x+h)-f(x)/h assuming that h ≠ 0

Algebra ->  Functions -> SOLUTION: If f(x)= -2/x+3, what would be the simplest form of f(x+h)-f(x)/h assuming that h ≠ 0      Log On


   

Question 1094525: If f(x)= -2/x+3, what would be the simplest form of f(x+h)-f(x)/h assuming that h ≠ 0
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
%28f%28x%2Bh%29-f%28x%29%29%2Fh=[f(x+h)-f(x)]/h is the average rate of change of the function between x and x%2Bh .

For f%28x%29=+-2%2Fx%2B3 , with h%3C%3E0 , it is
%28f%28x%2Bh%29-f%28x%29%29%2Fh%22=%22%28-2%2F%28x%2Bh%29%2B3-%28-2%2Fx%2B3%29%29%2Fh%22=%22%28-2%2F%28x%2Bh%29%2B3%2B2%2Fx-3%29%2Fh%22=%22%28-2%2F%28x%2Bh%29%2B2%2Fx%29%2Fh%22=%22%28-2x%2F%28x%28x%2Bh%29%29%2B2%28x%2Bh%29%2F%28x%28x%2Bh%29%29%29%2Fh%22=%22%28%28-2x%2B2x%2B2h%29%2F%28x%28x%2Bh%29%29%29%2Fh%22=%222h%2F%28x%28x%2Bh%29h%29%22=%22highlight%282%2F%28x%28x%2Bh%29%29%29%22=%22highlight%282%2F%28x%5E2%2Bxh%29%29
For this problem, the meaning of "simplest" is whatever the teacher thinks it is.
As the expression %28f%28x%2Bh%29-f%28x%29%29%2Fh is used to introduce the concept of derivative,
I would expect that %28f%28x%2Bh%29-f%28x%29%29%2Fh2%2F%28x%5E2%2Bxh%29 is what the teacher had in mind.

NOTE: When you type expressions into a computer or calculator,
you should make sure you type the parentheses that were implied in those long fraction bars we can write on paper:
%28f%28x%2Bh%29-f%28x%29%29%2Fh=[f(x+h)-f(x)]/h , but f(x+h)-f(x)/h=f%28x%2Bh%29-f%28x%29%2Fh ,
-2/x+3=-2%2Fx%2B3 , and -2%2F%28x%2B3%29=-2/(x+3)
Forgetting to type some of those parentheses implied by other grouping symbols may lead to wrong results.
If you type "0.732-0.002/0.713-0.003" into a calculator, you are likely to get
0.732-0.002/0.713-0.003=0.732-0.002%2F0.713-0.003 , and that is approximately 0.732-0.002805049-0.03=approximately0.7261974951 ,
because most calculators know about order of operations.
If what you meant was
(0.732-0.002)/(0.713-0.003)=%280.732-0.002%29%2F%280.713-0.003%29=0.730%2F0.710=approximately1.028169014 ,
you got the wrong result.