Question

Last few Calculus questions

Answer 1

gah ... i'm gonna cheat and assume\[f=5(x-3) +4\]

Answer 2

\[(f^{-1})'(x)=\frac{1}{f'(f^{-1}(x))} \\ \text{ you can replace } f^{-1} \text{ with } g\]

Answer 3

\[(f^{-1})'(x)=\frac{1}{f'(f^{-1}(x))}\]

Answer 4

i must be getting slow....

Answer 5

f(3) = 4

... so, g(4) =3

ok... ok ...ok

Answer 6

Ok many equations I see

Answer 7

Which one am I following guys?

Answer 8

either

Answer 9

\[(f^{-1})'(x)=\frac{1}{f'(f^{-1}(x))} \\ \text{ you can replace } f^{-1} \text{ with } g\]

\[g'(4)={1\over f'\left( g \left( 4 \right) \right)}\]

Answer 10

I'm getting something weird

Answer 11

did you use what pax said above that f(3)=4 implies g(4)=3 ?

Answer 12

I saw it but I'm not really sure how to work that in

Answer 13

\[g'(4)=\frac{1}{f'(\color{red}{g(4)})}\]

Answer 14

g(4) = 3

f'(g(4) = f'(3)=5

Answer 15

do you see g(4) now?

Answer 16

Yes I saw that part

Answer 17

OH

Answer 18

Is it one of the 3/5's?

Answer 19

dfg.bdflgd b......


i seem to be getting 1/5

Answer 20

Well I'm pretty slow so you're most likely right

Answer 21

Hey Pax can you check an answer for me as well?

Answer 22

I know the one selected isn't right but it has to be one of the bottom three I know that far lol...

Answer 23

\[g'(4)=\frac{1}{f'(\color{red}{g(4)})}\]

if this formula is too daunting

you can you can just write some equation for f that satisfies all the conditions, like
\[f: y= 5(x-3)+4\\=5y-11\]

to get the equation of g you just swap y and x
\[x=5\left( y-3 \right)+4\]
or \[y=\frac15\left( x-4 \right)+3\\=\frac15x+2\frac15\]

slope=1/5

Answer 24

Makes much more sense now lol thank you Pax

Answer 25

in all the charts ... wherever it says f'(x) ... it should be f(x)

Answer 26

critical values means all the relative minimums and maximums

Answer 27

Got it

Answer 28

still doesn't make sense....

Answer 29

if the table is supposed to be vales of f(x)

... the first two values in option B are correct 2, -4, -2
.... just the last value has to be between -5 and -3 ... can't be -2.

Answer 30

hmmmm

Answer 31

if the chart is showing derivatives \(f'(x)\) then the question should say so... and the first option you have chosen could be correct

Answer 32

Oh :) So should I go that route?

Answer 33

idk... you said you knew that wasn't right

Answer 34

Considering the fact that all of the majority where 2's and 4 based.

Answer 35

Ah whatever