Question

derivative question, can anyone help? It's very hard...

http://puu.sh/1f2NQ

Answer 1

WHAT IS?

Answer 2

link in description

Answer 3

guys pleeeasse help I've been trying to figure this out for an hour with no success :SS

Answer 4

Yea, no thanks. I'm not following some shortened URL off site to find you're problem. Post here if you want help.

Answer 5

What is it? Most likely a link to a virus.

Answer 6

YIPES HURRY UP AND GET YOUR CAPS LOCK FIXED. What can you tell me of y' at 9? I will help you if you need it but I would like to walk you through the steps.

Answer 7

At x=9, the equation of the tangent line to the graph of y=g(x) is 2x+11y=−37

What is the equation of the tangent line to y=g(x^2) at x=3 and the equation of the tangent line to y=(g(x))^2 at x=9?

Answer 8

TRY FIGURE OUT y

Answer 9

@whatisthequestion its -2/11

Answer 10

i found out that g(9)=-5 and g'(9)=-2/11, but im stuck here don't know where to go next :S

Answer 11

-x/y shortcut you can use that too...

Answer 12

can anyone help :S

Answer 13

hmm this is actually harder then I originally thought at your current time in class are their any restrictions on what g(x) could be eg. it has to be linear because otherwise at first glance their appears to be infinitely many solutions varying from simple lines to parabolas to circle to piece wise to all the other types of fucntions

Answer 14

they say there is only 1 solution

Answer 15

I would strongly argue that because if g(x) is a piece-wise function, and I see no reason why it could not be, then I can draw a graph that has a linear function at that point but at x^2 has no value approaching infinity on either side which of course would be different then just the linear function alone.

Answer 16

anyways I am sorry but I must not see this question the way your instructors do and as such I cannot come up with a way to solve it I am very sorry for wasting your time but a hint of advice if you truly have to hand something in and cannot come up with an answer think of it as a linear function. The slope of the tangent will remain constant as the slope of the graph remains constant and you have a point on the line which you can use to form the orginal g(x) which makes this question much much simpler

Answer 17

\[
\ \ \ 2x+11y=-37\\
\ \ \ 11y=-2x-37\\
\ \ \ y=-\frac{2}{11}x-\frac{37}{11}\\
\ \ \ g'(9)=-\frac{2}{11}\\
\ \ \ g(9)=-\frac{6}{11}-\frac{37}{11}=\frac{31}{11}\\
\text{Now, let's try the first one.}\\
\ \ \ y(x)=g(x^2)\\
\ \ \ y'(x)=2x\ g'(x^2)\\
\ \ \ y'(3)=6g'(9)=-\frac{12}{11}\\
\text{... so our tangent line is (point-slope form)}\\
\ \ \ Y-y(3)=y'(3)[x-3]\\
\ \ \ Y-g(9)=-\frac{12}{11}(x-3)\\
\ \ \ Y-\frac{31}{11}=-\frac{12}{11}(x-3)\\
\text{... and the second one is identical process.}\\
\ \ \ y(x)=[g(x)]^2\\
\ \ \ y'(x)=2g(x)g'(x)\\
\ \ \ y'(9)=2g(9)g'(9)=2(\frac{31}{11})(-\frac{2}{11})=-\frac{124}{121}\\
\ \ \ Y-y(9)=y'(9)[x-9]\\
\ \ \ Y-[g(9)]^2=-\frac{124}{121}[x-9]\\
\ \ \ Y-\frac{961}{121}=-\frac{124}{121}[x-9]
\]

Answer 18

Woops, I made an error computing g(9), so the constants are all wrong... but the procedure is correct.

Answer 19

np its perfect.. i get it now.. thank u guys so much!!

Answer 20

Mind if I ask though. If you consider the possibility of other types of functions wouldn't this problem have infinite soultions. Or was I just going crazy earlier?

Answer 21

\[
\ \ \ 2x+11y=-37\\
\ \ \ 11y=-2x-37\\
\ \ \ y=-\frac{2}{11}x-\frac{37}{11}\\
\ \ \ g'(9)=-\frac{2}{11}\\
\ \ \ g(9)=-\frac{18}{11}-\frac{37}{11}=5\\
\text{Now, let's try the first one.}\\
\ \ \ y(x)=g(x^2)\\
\ \ \ y'(x)=2x\ g'(x^2)\\
\ \ \ y'(3)=6g'(9)=-\frac{12}{11}\\
\text{... so our tangent line is (point-slope form)}\\
\ \ \ Y-y(3)=y'(3)[x-3]\\
\ \ \ Y-g(9)=-\frac{12}{11}(x-3)\\
\ \ \ Y-5=-\frac{12}{11}(x-3)
\]
The idea is the same for the second function too.

Answer 22

sorry about the typo solutions

Answer 23

np man

Answer 24

It doesn't matter what g is really, all the relevant stuff we need to know is that 2x+11y=-37 intersects y=g(x) at x=9 and that the slope of 2x+11y=-37 is g'(9)