Question

screen shot attached

Answer 1

ick

Answer 2

:(

Answer 3

find the derivative, plug in the number, use the point slope formula

Answer 4

wanna do it step by step, or can we cheat?

Answer 5

there is an easier way I'm all for it lol

Answer 6

cheat :)

Answer 7

first we find the derivative
http://www.wolframalpha.com/input/?i=64x%2F%28x^2%2B64%29

Answer 8

:)

Answer 9

then we evaluate at \(x=-4\)
http://www.wolframalpha.com/input/?i=-%2864+%28-64%2Bx^2%29%29%2F%2864%2Bx^2%29^2%2C+x%3D-4

Answer 10

i love wolfram :)

Answer 11

then we use the formula after evaluating at x=4

Answer 12

-4

Answer 13

http://www.wolframalpha.com/input/?i=slope+12%2F15+through+%28-4%2C-16%2F5%29

Answer 14

thats my final answer y=4x/5?

Answer 15

Cheaters hehehe

Answer 16

hey you, I've never used that page its my first time cheating

Answer 17

you want to take that derivative, evaluate at \(-4\) etc
donkey work

Answer 18

if you really want to do things very quickly, you can plot the function f(x) in geogebra, then plot the point (-4,f(-4))

then after those 2 things are down, you can use the tangents feature to get the equation/graph of the tangent line

Answer 19

okay now I'm lost ... lol

Answer 20

but ideally you should know how to do a problem like this and use tools like wolfram alpha and geogebra as a way to check your answer

Answer 21

why don't you do it with
the point slope method, you are looking for the tangent line at a point

Answer 22

can you show me?

Answer 23

well you know how to find the slope using limit process do you?

Answer 24

no,i do not

Answer 25

jim!!! you're back :)

Answer 26

Actually I'm not sure if the question requires to not use the derivative
like @satellite73 used it

Answer 27

yes, ideally i think i'll be using wolfram to check my answers

Answer 28

@satellite73 is super smart too, maybe he approached the question a different way, but still get the correct answer

Answer 29

yes you need the derivative to find the slope
there is not other way to do it

Answer 30

but to take the derivative you need the quotient rule
it is not impossible, but no fun
we can do it if you like step by step

Answer 31

okay sounds!!

Answer 32

First we need the derivative (use the quotient rule)

\[\Large f(x) = \frac{64x}{(x^2+64)}\]

\[\Large f^{\prime}(x) = \frac{64(x^2+64)-64x(2x)}{(x^2+64)^2}\]

\[\Large f^{\prime}(x) = \frac{64x^2+4096-128x^2}{(x^2+64)^2}\]

\[\Large f^{\prime}(x) = \frac{4096-64x^2}{(x^2+64)^2}\]

-------------------------------------------------------

Then plug in x = -4 to find the slope of the tangent line at (-4,-16/5)

\[\Large f^{\prime}(x) = \frac{4096-64x^2}{(x^2+64)^2}\]

\[\Large f^{\prime}(-4) = \frac{4096-64(-4)^2}{((-4)^2+64)^2}\]

\[\Large f^{\prime}(-4) = \frac{12}{25}\]

-------------------------------------------------------

Use this slope, and the point (-4,-16/5), to get the equation of the tangent line

\[\Large y = mx+b\]

\[\Large y = \frac{12}{25}x+b\]

\[\Large \frac{-16}{5} = \frac{12}{25}(-4)+b\]

\[\Large \frac{-16}{5} = -\frac{48}{25}+b\]

\[\Large \frac{-16}{5}+\frac{48}{25}=b\]

\[\Large -\frac{32}{25}=b\]

So that's why the equation of the tangent line is

\[\Large y = \frac{12}{25}x-\frac{32}{25}\]

Answer 33

lol i was hoping you would say no
\[\left(\frac{f}{g}\right)'=\frac{g'f-f'g}{g^2}\] with \[f(x)=64x,f'(x)=64,g(x)=x^2+64, g'(x)=2x\]

Answer 34

it should be f' * g - g' * f

Answer 35

@jim_thompson5910 Wow thank you!!! the derivative part i kinda get now, i can actually practice them and check them with wolfram, thank you:)

Answer 36

yeah i messed up

Answer 37

not sure what you mean satellite73

Answer 38

oh ok

Answer 39

\[\left(\frac{f}{g}\right)'=\frac{gf'-fg'}{g^2}\]

Answer 40

@satellite73 ahhh I'm sorry!!!:( i'll try to practice more so you won't have to go step by step that much !:) Thanks to you too!!

Answer 41

thats my final answer right? y=12/25x 32/25

Answer 42

\[\Large y = \frac{12}{25}x-\frac{32}{25}\]

Answer 43

with a minus sign

Answer 44

thank you guys!!! It was correct, as usual!! lol

Answer 45

I'm going to screen shot all the steps and practice those lol

Answer 46

@sateliite!!!

Answer 47

you write satellite73 after an @ symbol, so @satellite73

you have to use the full name with numbers and everything (matching it up perfectly) for it to work

Answer 48

and if you're trying to get the attention of other mods, you can message anyone who has a purple avatar/icon (they should have "moderator" under their names)

Answer 49

@satellite73
help me

Answer 50

:) Thank you, always help me with everything! @jim_thompson5910

Answer 51

np