Question

Let k(x) = (f(x))^−1. find k'(2) given a tangent line with points (5,2) and (2.1,5.3) and the line of f(x) hitting (5,2)

Answer 1

Hey there :)
Hmm that first one is a little tricky.

Answer 2

Do you get unlimited guesses?
I wanted to test an answer and see if I figured it out correctly.

Answer 3

I can explain it also, I just don't want to explain it if I did incorrectly :) lol

Answer 4

I have 2 guesses left

Answer 5

Ah ok :c well here is what I did.

Answer 6

Mmm hold up I gotta rethink that >.<
Grr tricky tricky.

Answer 7

oh oh oh ok here we go... i think

Answer 8

\[\Large\rm k(x)=\frac{1}{f(x)}\]Taking derivative gives us,\[\Large\rm k'(x)=-\frac{f'(x)}{f^2(x)}\]We can use the points given to evaluate f'(x), yes?

Answer 9

\[\Large\rm f'(2)=\frac{5.3-5}{2.1-2}\]\[\Large\rm f(2)=5\]That should give us everything we need.

Any confusion on that? :O

Answer 10

The negative in the first problem looks like its indicating a `reciprocal`, not in inverse.

Answer 11

ok i follow

Answer 12

So run the numbers!! :)
Tell me what you get before you throw it into the thing! :O
You don't wanna burn guesses!

Answer 13

what does f^2 of x mean just f(x) squared?

Answer 14

Yah I was being a lil fancy, my bad.\[\Large\rm f^2(x)=\left[f(x)\right]^2\]

Answer 15

would the answer be -3/25

Answer 16

Yayyyy good job \c:/
That's what I'm coming up with also.

Let's give it a try.

Answer 17

moment of truth scared face

Answer 18

XD

Answer 19

you my friend are a savior praise (300 chant) Ah-oooo Ah-oooo

Answer 20

yay team!

Answer 21

thanks again greatly appreciate it.