Question

Given: (below) what is a reasonable value for d/dx h^-1 (x), evaluated at x = 5?

Answer 1

3
1/3
1
-3
-1/3

Answer 2

wow, there is one of those questions. Dang

Answer 3

@SithsAndGiggles

Answer 4

@dan815

Answer 5

let me try to refer some people

Answer 6

@Michele_Laino

Answer 7

Hey, Michele, can you help this person out?

Answer 8

I try!

Answer 9

Alrightly!

Answer 10

@Michele_Laino you still there?

Answer 11

I think the system bugged out. Everybody went offline.

Answer 12

hmmm...
\[(h^{-1})'(x)=\frac{1}{h'(h^{-1}(x))} \\ (h^{-1})'(5)=\frac{1}{h'(h^{-1}(5))}\]
we can find h inverse of 5 from the table

Answer 13

I think Nathan is offline.

Answer 14

Well if @NathanJHW returns
and I'm not here
I will give another hint

Look at the data and think lines
find the slope of the line (that is the key )

Answer 15

Freckles how often are you online daily?

Answer 16

sometimes none
sometimes a few
I would say I guess I might average at min 2 hours a day

Answer 17

ah i see.

Answer 18

I got the subsequent stes:

\[\Large \frac{{dh}}{{dx}} = \frac{1}{{\frac{{dx}}{{dh}}}} = \frac{1}{{\frac{{d{h^{ - 1}}}}{{dy}}}}\]

Answer 19

since:
\[y = h\left( x \right),\quad x = {h^{ - 1}}\left( y \right)\]

Answer 20

ahahah go on.

Answer 21

@NathanJHW

Answer 22

so we can write:
\[\Large {\left. {\frac{{d{h^{ - 1}}}}{{dy}}} \right|_{y = 5}} = \frac{1}{{{{\left. {\frac{{dh}}{{dx}}} \right|}_{x = 1}}}}\]
and what is \[{{{\left. {\frac{{dh}}{{dx}}} \right|}_{x = 1}}}\]?

Answer 23

it is very simple:
\[\Large {\left. {\frac{{dh}}{{dx}}} \right|_{x = 1}} = \frac{{1.0 - 0.9}}{{5.0 - 5.3}} = \frac{{1.1 - 1.0}}{{4.7 - 5.0}} = ...?\]

Answer 24

1/3

Answer 25

yes!

Answer 26

thank you!

Answer 27

so what is the right option?

Answer 28

Ites actually -1/3

Answer 29

no wait, somethings wrong.

Answer 30

no, we have to compute this:
\[\Large {\left. {\frac{{d{h^{ - 1}}}}{{dy}}} \right|_{y = 5}} = \frac{1}{{{{\left. {\frac{{dh}}{{dx}}} \right|}_{x = 1}}}} = \frac{1}{{1/3}} = ...?\]

Answer 31

3?

Answer 32

that's right!

Answer 33

I guess thats it. There you go Nathan. Thank you Michele! Your such a helpful person.

Answer 34

Thank you :) @keepo @NathanJHW @freckles

Answer 35

Its not me who needs thanking, its you Michele.

Answer 36

ok! :)

Answer 37

because we have 1/(-1/3)

Answer 38

not 1/(1/3)

Answer 39

but yeah the function is decreasing so it h'<0

Answer 40

So the answer is?

Answer 41

you just need to find the reciprocal of -1/3
that is the meaning of 1/(-1/3)

Answer 42

So its -3.

Answer 43

yeah

Answer 44

What did Michele do wrong?

Answer 45

he made a small arithmetic error in finding the difference

Answer 46

ah i see

Answer 47

anyways yeah all he did was attempt to find the slope of the line
which I though @NathanJHW would get to do but I guess @michele_laino didn't want to given him the chance to :p