Question

need help with a conjugate

Answer 1

\[f(x)=\sqrt{3-x}\]

Answer 2

I am doing (f(x+h) - f(x))/h difference quotient

I know it should be 1/2 (3-x)^(1/2)
bu I am getting a negative one not positive one for the numerator
can't seem to find my error

Answer 3

let me type what I have and see if you can help me find my mistake

Answer 4

Ok take your time. =)

Answer 5

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

Answer 6

\[\frac{ \sqrt{3-x-h}-\sqrt{3-x} }{ h }\]

Answer 7

if I multiply by the conjugate \[\sqrt{3-(x+h)}+\sqrt{3-x}\]

Answer 8

of course multiply to the top and bottom

Answer 9

Ok good.

Answer 10

\[\frac{ -h }{ h \left( \sqrt{3-x-h}+\sqrt{3-x} \right) }\]

Answer 11

but shouldn't that h on top be positive
I only know this because I am really just taking the derivative of \[\sqrt{3-x}\]

Answer 12

I like to double check myself whenever possible

Answer 13

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

Answer 14

Well by the chain rule, won't you end up with a negative because the derivative of -x is -1?

Answer 15

if I sub h=0 because the limit approaches zero at this point I get
\[\frac{ -1 }{ 2\sqrt{3-x}}\]

Answer 16

Yep, that's the correct answer. =)

Answer 17

you are very right, I forgot the derivative of the inside. I need some coffee this morning. thanks

Answer 18

Haha no problem. I think overall you have a good method and you should continue to cross check yourself like this as it's very wise. Often times my "sanity checks" will feel like "insanity checks" but when I find out it's something like this I always sort of feel like slapping myself in the head for not seeing something that's almost obvious haha. Keep up the good work!

Answer 19

thanks and I also, need to be alert. I knew I wasn't too wrong but something it is hard to find a small mistake.

Thanks so much