Question

Find the derivative of f(x) = 6/x at x = -2.

Answer 1

@agent0smith

Answer 2

Do it the same way as the last,

f'(x) = (f(x+h) - f(x))/h

this time, f(x+h) = 6/(x+h)

f'(x) = ( 6/(x+h) -6/x)/h

You'll have to simplify those fractions, though...

Answer 3

oh poop lolol

Answer 4

Yeah I don't really want to try it w/o the equation editor....

Answer 5

easier to read: http://www.wolframalpha.com/input/?i=simplify+6%2F%28x%2Bh%29+-6%2Fx

Answer 6

Now if you divide that result by h, then plug in h=0, you'll have the derivative

Answer 7

http://www.codecogs.com/latex/eqneditor.php
You can make links or images from that. Just be sure to make the background white.

Answer 8

-6 ?

Answer 9

I think you made a small mistake in simplifying.

Answer 10

http://www.wolframalpha.com/input/?i=simplify+%28+6%2F%28x%2Bh%29+-6%2Fx%29%2Fh

now plug in h=0 into either of those simplified results. (the derivative is really the limit as h approaches zero)

Answer 11

wait 6? lol

Answer 12

-6/(hx + x^2)

plug in h=0

Answer 13

i gots -6/x^2

Answer 14

AH HA! that looks better.

Answer 15

Yes :)

Answer 16

Now evaluate at f'(-2)

Answer 17

so would i put x=-2^2

Answer 18

f'(x) = -6/x^2

plug in x=-2

Answer 19

-6/-2^2

Answer 20

well, x=-2, not -2^2. It will be squared, but not before you plug it in.

Answer 21

Yah, -6/(-2)^2

Answer 22

i got -1.5

Answer 23

Correct :)

Answer 24

Now you may not have known what my whole tangent line thing was. This is what it would look like in this case:
https://www.desmos.com/calculator/jvebfrvtvj

I doubt you are doing those yet, but just thought I would show how the whole knowing point-slope formula comes into play later as you get into calculus.

Answer 25

so 3/2?

Answer 26

well-3/2

Answer 27

Yah. -3/2, whch is -1.5.

Answer 28

@e.mccormick and @agent0smith THANK YOU SO MUCH GUYS!!♥

Answer 29

Welcome ♥

Answer 30

np. Have fun.

And I hope you can see how calculus depends on algebra, so all that learning you did before this will come into use later. Well, calculus is used in medicine, physics, engineering, and so on, so everything it takes to learn calculus comes into play in doing so many other things. Well worth understanding it for that.