Question

Find equation of tangent line and normal line?

Answer 1

http://assets.openstudy.com/updates/attachments/56218da7e4b0b85f3a1503dd-babynini-1445039542489-capture.png

Answer 2

Value of y' at 0.01 is = 1/25, I think.

Answer 3

@Miracrown

Answer 4

\[y-y_1=M(x-x_1)\]Where M is the slope of the tangent line

Answer 5

Did you get the function for y' ?

Answer 6

Yes, well, I got the derivative of the first y equation thing.

Answer 7

what di dyou get?

Answer 8

\[y'(x)=\frac{ \frac{ x+9 }{ 2\sqrt{x} }-\sqrt{x} }{ (x+9)^2 }\]

Answer 9

\[y ' = \frac{ -(x-9) }{ 2\sqrt{x}*(x+9)^2 }\]

Answer 10

equivalent, yeah? maybe yours is easier to work with xD

Answer 11

i just put it in my calculator, lol sorry

Answer 12

quotient rule, bottom times derivative top minus top times derivative bottom, all over bottom squared

Answer 13

Why do we need to do the quotient rule if we already have the derivative?

Answer 14

ooh right, I see what you're saying. Yep, that's what I did haha

Answer 15

ok, the point given on the function is (x,y) = (1 , 0.1)

use that in the derivative, and y' will tell you the slope of the tangent line there at the point

Answer 16

like plug x into the derivative?

Answer 17

yeah figure out f ' (x) =

Answer 18

k, well I think f(1) = 1/25

Answer 19

yes,

the value of the derivative at any point is the slope of a tangent line to the function at tha tpoint, so the tangent line has slope 1/25, and goes through the given point (x,y)

make a line equation from that

Answer 20

the normal is perpendicular to a tangent at some point, just use the perpendicular slope to 1/25 and the same point for the normal line

Answer 21

hmm is it
y = 1/25x-0.14?

Answer 22

tangent line :

y - y1 = f '(x) *(x - x1)


normal line, same, cept slope is -1/f'(x)

Answer 23

or
y= 0.04x-0.14 for the tangent line

Answer 24

so the normal would be..
y=-25x-0.14? o.o

Answer 25

just miscalculated i think ...

y - 0.1 = f '(x) *(x - 1)

Answer 26

I think your sign is off
y - 0.1 = (1/25)(x-0.1)
y - 0.1 = x/25 - 1/250

Answer 27

y = x/25 - 1/250 + 1/10 = 0.04x + 0.096

Answer 28

you can always graph everything and check if they look right,
https://www.desmos.com/calculator

Answer 29

Where did you get that big 250?!

Answer 30

gah im wrong

Answer 31

x,y) = ( 1 , 0.1)

Answer 32

tangent - x/25 - 0.06

Answer 33

y - 0.1 = (1/25)(x-0.1)****
y - 0.1 = x/25 - 0.04

Answer 34

OMG

Answer 35

hah

Answer 36

y - 0.1 = (1/25)(x-1)****
y - 0.1 = x/25 - 0.04

Answer 37

when you add 0.1 to 0.04 it equals 0.14 though..

Answer 38

y = x/25 - 0.04 + 0.1

Answer 39

so youre actually subtracting .04 from .1

Answer 40

ooh I see i see.

Answer 41

And then the normal is the same, except -1/(1/25)

Answer 42

Which comes out to..

Answer 43

-25x-0.06 ??

Answer 44

lol yeah

-1/25 - 1/10 = 3/50 or about 0.06

Answer 45

plus 1/10 omg

Answer 46

lol long day for everyone

Answer 47

lol yeah

-1/25 + 1/10 = 3/50 or about 0.06

Answer 48

Oh my gosh, coffee break yall.

Answer 49

You guys are doing excellent! no worries!! We can do this! xD

Answer 50

screw the arithmatic, as long as you get the concepts

Answer 51

but I gotta turn this in ..hehe
normal = -25x-0.06 ?

Answer 52

three tired brains is better than 1 tired brain i suppose - at least we catch everyone else's mistakes

Answer 53

you find a function for the slope (derivative), calculus over

Answer 54

finish with algebra

Answer 55

asfpaig the thing says both answers are wrong :(

Answer 56

graph them and see what it looks like

Answer 57

for the normal, same point and inverse negative slope, m = -25, point (1, 0.1), calculate that line again

Answer 58

not sure maybe all decimals or all fractions wanted, syntax

Answer 59

oo maybe. so how do i do 0.06 in fraction=.=

Answer 60

35/250? haha

Answer 61

normal

y - 0.1 = -25*(x - 1)

Answer 62

y = 25.1 - 25x

Answer 63

y = -25x+25.1

Answer 64

haha yeah. So for the tangent it would be?

Answer 65

tan : 0.04x-0.06

Answer 66

Nope, it didn't like that.

Answer 67

AHA
I GOT IT

Answer 68

oh dude, we got it at the same time lol.
idk why i had the 0.06 negative.

Answer 69

...and nvm, I misread the problem xD

Answer 70

You guys are amazing <3 thanks for staying with me lol

Answer 71

yeah, dumb computer checking tools

i guess you should choose decimal or fraction, and have to stay the same for everything

Answer 72

welcome, if you have another similar, i am sure it will be done in 2 or less responses, i promise

Answer 73

Right. Quick question though
how come it had to be put in as
25.1-25x rather than -25x +25.1 ?

Answer 74

aw thank you:) i'm all done for today!! Though I should probably do some practice ones o.o clearly.

Answer 75

sorry was afk

Answer 76

i dont know, whoever programmed the thing did it

Answer 77

just always lead with a positive value if you can , i guess