Question

Find an equation for the line tangent to the graph of
f(x) = \frac{e^{6 x}}{8 x - 1}
at the point (3, f(3)).

Answer 1

\[Find an equation for the line tangent \to the graph of f(x) = \frac{e^{6 x}}{8 x - 1} at the point (3, f(3)). \]

Answer 2

The slope at a point is determined by the derivative at that point. Find such derivative and use point-slope to create this line to be tangent to the graph.

Answer 3

OKay so get the derivative and plug in the points for the slope?

Answer 4

Yes, plug in \(x=3\) to the derivative for the slope, and then use point-slope formula:
\[
y-y_0=m(x-x_0)
\]To create such a line (where \(y_0=f(3), x_0=3\))

Answer 5

Thanx

Answer 6

The derivative is messy for m

Answer 7

Hello!~~~~~~

Answer 8

yes... I agree

Answer 9

Did you get a nice complicated m once you plugged in your numbers?

Answer 10

I got\[\frac{130e ^{18}}{529}\]

Answer 11

but f(3) is equally complicated, so maybe the complications will cancel out in the equation for the line.

Answer 12

yea and I dont know if anything is right

Answer 13

so what did you get for the answer?

Answer 14

f(3)=\[\frac{e ^{18}}{23}\]

Answer 15

for the equation?

Answer 16

For the line\[y- \frac{e ^{18}}{23}= \frac{130e ^{18}}{529}(x-3)\]

Answer 17

in y=mx+b form

Answer 18

Distribute, take the e term over to the right, find a common denominator and combine like terms.... what did you get? :)

Answer 19

Stop making me learn just give me the answer. haha

Answer 20

I'm mean that way. :)

Answer 21

Did you read my testimonial for you?

Answer 22

No

Answer 23

click on your icon, then click on it in the little window, then find testimonials on the left and click on the number

Answer 24

haha

Answer 25

Your score was about 16 when we started today... look now... you have double that!

Answer 26

yay!

Answer 27

Now if only i could finish my homework

Answer 28

k... now I gave you the point slope form for your problem... simplify it... you're in calculus... you can do it!

Answer 29

Algebra is the hardest part of calculus.

Answer 30

okay

Answer 31

um........

Answer 32

im trying to get b with this

Answer 33

yeah, yeah, um.... I sat by your last post for 35 minutes before I realized that you had moved on to this question. I hope that you got the last one right. Yeah b is the hardest part.

Answer 34

\[\frac{ e^{18} }{ 23}=\frac{ 130e ^{18} }{529}(3) +b\]

Answer 35

no?

Answer 36

You did? Sorry, haha.

Answer 37

My bad

Answer 38

no biggie... this post is so long... my LaTeX stopped working... just a sec.

Answer 39

just for fun...here is the graph

https://www.wolframalpha.com/input/?i=plot+e^%286x%29%2F%288x-1%29%2C+%28e^18%2F529%29%28130x-367%29+from+2.5+to+3.5

Answer 40

nope... that's not it. haven't looked at @dumbcow 's link yet

Answer 41

doh! that gives it away a little...

Answer 42

alright... I'll do some more...

Answer 43

ahhhhhhhhhhhhhhhhhhhhhhh

Answer 44

yeah sorry about that....anyway @monique.awesome , your equation is good just solve for b

Answer 45

\[y= \frac{130e ^{18}}{529}x- \frac{390e ^{18}}{529}+ \frac\]\[y=\frac{130e ^{18}}{529}x - \frac{367e ^{18}}{529}\]I f your LaTeX is lagging like mine... I will at least force you to read LaTeX.... Learning!

Answer 46

-\[-\frac{ 367 }{ 529}e ^{18}\]

Answer 47

I was working on it!

Answer 48

Hey look sI got b yay!

Answer 49

woof!

Answer 50

I think... was it -(367e^18)/529?

Answer 51

Thats what I got now I have to figure out how to put that crap in my program haha

Answer 52

good luck!

Answer 53

Oh no! Now you will use Wolfram Alpha. Be careful! It's bad for your learning if abused.

Answer 54

Wha?

Answer 55

I figured it out!

Answer 56

nothing....

Answer 57

You truly deserve awesome in your name.

Answer 58

Sorry I have to take ths part of calculus for my degree

Answer 59

but my last calculus class was two semesters ago

Answer 60

Aw thanx

Answer 61

What!?! This isn't just for fun?

Answer 62

haha

Answer 63

I wish

Answer 64

Okay I post new question

Answer 65

k