Question

Hey how do you do the definition of sqrt(3x+1)??

Answer 1

\[\sqrt{3x}+\sqrt{1}\]

Answer 2

is this what you are looking for?

Answer 3

@rrp240 you are wrong
@MathGeekinProgress : your question isn't clear to me

Answer 4

No I'm supposed to put this into [f(x+h) - f(x)] all over h aka definition form

Answer 5

Definition of a derivative we mean then

Answer 6

definition -> derivation

Answer 7

:P

Answer 8

Well, we literally would replace every x in our function with x+h and then just write it out as the formula describes:

\[\frac{ \sqrt{3(x+h)+1} -\sqrt{3x+1}}{ h }\]
From here, you would be forced to multiply top and bottom by the conjugate, which is eseentially taking the whole numerator and changing the middle sign into a plus. So it would look like this:

\[\frac{ \sqrt{3(x+h)+1} - \sqrt{3x+1} }{ h }*\frac{ \sqrt{3(x+h)+1} + \sqrt{3x+1} }{ \sqrt{3(x+h)+1} + \sqrt{3x+1} }\]

Answer 9

Ok

Answer 10

If you can multiply out and simplify the top properly, it shouldnt be too bad. It is messy, so maybe as a tip to try and multiply it out safely (only a suggestion), know that:
\[(a+b)(a-b) = a^{2} - b^{2}\]If you undersrand that, it makes it easy to foil out the top without much trouble.

Answer 11

So the sqrt symbols on the top will go away since we are basically squaring it. So we would come to this:
\[(3h + 2) / (h(\sqrt{3x+3h+1} - \sqrt{3x+1})\]

right?