Question

Hi! I will fan and medal, I just really need help. Okay so the question is estimate the rate of change at x=2 for y(x)=1/(x+2).... my answer is attached, but I am informed that I am wrong. What am I doing wrong? My teacher gave me answers that go out to 3 decimals, but when I simplify the slopes in the middle column all I get is to the tenth. Help please!!

Answer 1

HI!!

Answer 2

don't see the attachment, but you could try taking the slope between \((2,\frac{1}{4}\)) and \((2.1,\frac{1}{4.1})\)

Answer 3

or if you want to get more precise, use \[(2,\frac{1}{4}), (2.001,\frac{1}{4.001})\]

Answer 4

The rate of change is \[
-\frac 1 4\] at x=2

Answer 5

Hi @misty1212 just saw this, let me attach my picture again and see if it will work, and through this can you help me?

Answer 6

@agent0smith Hi! Sorry to always bug you... but can you help me with this??

Answer 7

I don't know what you're doing wrong (possibly your calculations are off), but the slope should approach -1/16 or -0.0625

Answer 8

Yeah, your calculations are off somewhere:
http://www.wolframalpha.com/input/?i=(1%2F(1.9999%2B2)-1%2F4)%2F(1.9999-2)

Answer 9

That is so weird, I am inputting it exactly as I wrote it into my calculator! Is there a setting in calculators which round the answers that I am receiving? @agent0smith

Answer 10

But the values you input might be wrong... the one i posted above is exact

Answer 11

You're rounding too much is my guess:
http://www.wolframalpha.com/input/?i=1%2F(1.9999%2B2)

Answer 12

That is so strange, because I am not rounding at all, it is coming out of my TI-84 like that...

Answer 13

Then use EXACT values when you type it in

Should look like this:
(1/(1.9999+2)-1/4)/(1.9999-2)

Answer 14

And yes sometimes calculators have a setting to truncate and only show a certain number of decimals... but if you use exact values as above, and are careful with parentheses, you won't have that problem.

Answer 15

If you press Mode, you'll be able to see if it's not in a standard mode.

Answer 16

Argh, I still don't understand. For example, in the first interval from [2, 2.01], I would input first .25-.2494, which is equal to .0006. Then, I divide that by (2-2.01), which is -.06. So that would be my answer, would it not?

Answer 17

Yes that's right.

But i'm suggesting you do it exactly.

Slope is \(\Large \frac{y_2 - y_1 }{ x_2-x_1 }\) or \(\Large \frac{ f(b)-f(a) }{ b-a }\)

So slope from x=1.9999 to 2 is:
\[\huge \frac{ \frac{ 1 }{ 1.9999+2 }-\frac{ 1 }{2+2 } }{ 1.9999 -2 }\]

Answer 18

Oh yikes, and I was so confused! Thank you so much for this silly fix. :) @agent0smith

Answer 19

It makes sense now? Welcome :)