SOLUTION: finding the difference quotient f(x+h)-f(x)/h g(x)=3sqrt of x I can set it up but i can't get the right answer 3 sqrt x+h

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Question 344844: finding the difference quotient
f(x+h)-f(x)/h
g(x)=3sqrt of x

I can set it up but i can't get the right answer
3 sqrt x+h - 3sqrt of x/ h

Found 2 solutions by stanbon, jsmallt9:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
[f(x+h)-f(x)]/h
g(x)=3sqrt of x
---------------------------
f(x+h) = 3sqrt(x+h)
f(x) = 3sqrt(x)
----
[f(x+h)-f(x)]/h = [3[sqrt(x+h)-sqrt(x)]]/h
-------
Multiply numerator and denominator by sqrt(x+h)+sqrt(x) to get.
-----------
= (3/h)[(x+h)-x]/[sqrt(x+h)+sqrt(x)
---
= (3/h)[h]/[sqrt(x+h)+sqrt(x)
----
= 3/[sqrt(x+h)+sqrt(x)]
==========================
Notice, if you let h approach zero, the quotient approaches 3/(2x^(1/2))
= (3/2)x^(-1/2)
==================================
Cheers,
Stan H.

Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
You are exactly correct so far:

As h approaches 0, this is still of the 0/0 form so we need to do more. With experience you will learn that the next step is to multiply the numerator and denominator by . (You will see why after you see how this simplifies things.)

In the numerator we can take advantage of the pattern. (We'll leave the denominator factored for reasons you will see shortly.)

Simplifying the numerator:

At this point we will reduce the fraction. (And we can see why we didn't bother multiplying out the denominator.) The h's cancel:

We can factor out a 3 in the denominator:

And cancel a factor of 3:

This is the difference quotient. (As h approaches 0, this fraction is not of the 0/0 form.)

SOLUTION: finding the difference quotient f(x+h)-f(x)/h g(x)=3sqrt of x I can set it up but i can't get the right answer 3 sqrt x+h - 3sqrt of x/ h