Question

how can i solve this problem? please help me.. i've been stuck on it for days now !

Answer 1

do you know what g(x) is?

Answer 2

Euler's question is a good one. You can (or should be able to) obtain the function g(x) just from looking at the blue graph. What is the slope? What is the y-intercept?

Answer 3

Ooo fun problem :)

Answer 4

I guess finding your g(x) might be a good idea.
I would just use the chain rule and the slope of g(x) though.

\[\Large\bf\sf w(x)=g(g(x))\]\[\Large\bf\sf w'(x)=?\]Do you understand how to take this derivative?

Answer 5

Again, that blue line represents the function g(x), and again I suggest that you obtain that function before finding any derivatives.

Answer 6

so for a would you plug in 4 for x? ... so g(g(4)) ... but the derivative?

Answer 7

You can't plug 4 in until you've differentiated first.
Do you understand how to differentiate g(g(x))?

Answer 8

no

Answer 9

@skullofreak: I've twice suggested that you obtain g(x) from looking at the graph. Then, you need to differentiate g(g(x)).

Answer 10

Here's the definition of the chain rule to refresh your memory:\[\Large\bf\sf y=f(g(x)), \qquad y'=f'(g(x)\cdot g'(x)\]

Answer 11

You decide. If you want my advice, please determine g(x) from the graph.

Answer 12

I don't particularly like that method.
It's easier yes, but you really need to get comfortable with the chain rule.

Answer 13

It's one of the most confusing differentiation rules when you're early in calc, you really need to spend a lot of time with it :[

Answer 14

You take the derivative of the outer function, then multiply by the derivative of the inner function.
\[\Large\bf\sf y'=f'(g(x))\cdot g'(x)\]

Answer 15

What's confusing? the fact that we're not given an actual function?
It is it not specific enough so it's giving you trouble?

Answer 16

so i look at 4 then find the values for f(x) and g(x)? or how would i get the values/..

Answer 17

That was simply a definition.
In our case we have g(g(x)), not f(g(x)), so it will look a little different.

\[\Large\bf\sf w(x)=g(g(x))\]Using the definition for the chain rule,\[\Large\bf\sf w'(x)=g'(g(x))\cdot g'(x)\]You can plug in your 4 from here,\[\Large\bf\sf w'(4)=g'(g(4))\cdot g'(4)\]And then use the graph to fill in the pieces.

If this is way too confusing, then use male's method.
It will give you an actual function that you can differentiate instead of reading a graph.

Answer 18

Reading the graph,\[\Large\bf\sf g(4)=12\]So we'll plug that in,\[\Large\bf\sf w'(4)=g'(\color{orangered}{g(4)})\cdot g'(4)\]\[\Large\bf\sf w'(4)=g'(\color{orangered}{12})\cdot g'(4)\]

Answer 19

so 8(12(4))*8(4)?.

Answer 20

Ohh nvm

Answer 21

wait would derivative of g be 8 then? cause it is f(x)? or that has nothing to do with it

Answer 22

Hmm maybe I'm misunderstanding the question...
This doesn't appear to have ANYTHING to do with the f(x) that was graphed.

I can't figure out why it's there. :(

Answer 23

Is there a typo in the problem?
I think it's supposed to be w(x) = f(g(x))

or something like that... it would make a lot more sense.

Answer 24

hmm well theres 5 more problems like this and one has f(f(x)) too ..

Answer 25

Oh we use this same picture for a bunch of different problems?
Ok then it seems fine :)

Answer 26

We're just not using the f for any part of this.

Answer 27

no the graph is just for A,B and C the other questions have different graphs

Answer 28

o

Answer 29

like this one is f(f(x))

Answer 30

Ya I guess they do this sometimes in math problems.
They give you more information than you actually need.

Answer 31

The problem simplified to,
\[\Large\bf\sf w'(4)=g'(12)\cdot g'(4)\]
Now you need the slope of g at x=12, and the slope at x=4.
Since it's a linear function, both values will be the same (constant slope).

Answer 32

the derivative of g would be 8 then?

Answer 33

No. Hmm..
I'm not sure where you're getting 8 from.

See how the line slants `down` to the right?
It has a negative slope.

Answer 34

yes

Answer 35

Do you remember how to find the slope of a line.?

Answer 36

rise/run

Answer 37

Good.
So use a couple of points to find the slope.
I would recommend using the (16,0) and (0,16).

Answer 38

so... y2-y1/x2-x1 = 16-0/0-16

Answer 39

= -1

Answer 40

Yes, good!

Answer 41

g'(12) is the `slope` of g(x) at x=12.
And we're saying... that since it's a straight line, it has a slope of -1 everywhere.

Answer 42

Which means g'(12) = -1
and also g'(4) = -1

Answer 43

so the slope we get would be the derivative?

Answer 44

so there isnt a slope for the derivative of 8, but when i put DNE it says its wrong

Answer 45

because of the 'sharp corner'?

Answer 46

There is no sharp corner for the function g(x)

Answer 47

so a,b , and c would just be -1?

Answer 48

No none of them are -1.

Answer 49

oh yeah it was g(g(x)) we arent using f (x)

Answer 50

\[\Large\bf\sf w'(4)=g'(12)\cdot g'(4)\]\[\Large\bf\sf w'(4)=(-1)\cdot (-1)\]

Answer 51

oh ! okay okay i get it

Answer 52

But ya it looks like they all work out to the same value for a b and c.

Answer 53

yes b would be g'(8)*g'(8) = 1 again , ty so much! :) i can do the rest now !