Issy14
  • Issy14
Let w(x) = g(g(x)). Find: (a) w(1) (b) w(2) (c) w(3) somebody please help, I have no idea what to do.
Mathematics
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SOLVED
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katieb
  • katieb
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geerky42
  • geerky42
well, we need to know what g(x) is. were you given function of g?
Issy14
  • Issy14
@geerky42 one second going to post the image
Issy14
  • Issy14
|dw:1404857483770:dw|

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Issy14
  • Issy14
These are the directions: In Problems 57–60, use Figure 3.17 and the chain rule to estimate the derivative, or state why the chain rule does not apply. The graph of f(x) has a sharp corner at x = 2.
Issy14
  • Issy14
If you have time , I could really use assistance on this question. @TuringTest
Issy14
  • Issy14
@tkhunny If you have time, I could really use assistance on this question
Issy14
  • Issy14
I think i figured out g(x) = -1x+4 f(x) is not continuous it has a breat at (0,2) therefore if i try to get the slope they are going to have the same magnitude but different signs f(x)=4x or f(x)= -4x
Issy14
  • Issy14
I know the chain rule by heart, I don't know how to apply here. f'(x)= f'(g(x)) x g'(x)
Issy14
  • Issy14
Help in need of a mentor please. @Taylor<3sRin @myko @ganeshie8
Issy14
  • Issy14
help @jdoe0001
geerky42
  • geerky42
\(f(x) = -2|x-2|+4\)
geerky42
  • geerky42
hmm, wait. exactly what do you need help with?
Issy14
  • Issy14
with the problem given
Issy14
  • Issy14
it comes with the graph and the instructions.
Issy14
  • Issy14
How did you find f(x). ? did you just transform it from the original function |x|
Issy14
  • Issy14
@geerky42
geerky42
  • geerky42
yeah, that's how I figure it out
Issy14
  • Issy14
alright, is that the usual approach?
Issy14
  • Issy14
am I correct on g(x)?
geerky42
  • geerky42
well, i don't know what's your given problems are. are you asked to take derivative of f(x) using chain rule, or state why chain rule does not apply?
Issy14
  • Issy14
both In Problems 57–60, use Figure 3.17 and the chain rule to estimate the derivative, or state why the chain rule does not apply. The graph of f(x) has a sharp corner at x = 2. 60. Let w(x) = g(g(x)). Find: (a) w(1) (b) w(2) (c) w(3)
Issy14
  • Issy14
that's the problem and then they give you the graph
geerky42
  • geerky42
ok i see. well, we managed to figure f(x) out by using transformation from parent function, so we have f(x) = -2|x-2|+4 we can take derivative of f(x) because it is continuous. just not differentiable at break point. so we can let h(x) = -2x+4 and j(x) = |x-2| so we have \(f'(x) = h'(~j(x)~)~j'(x)\)
geerky42
  • geerky42
PS: \[\large\dfrac{d}{dx}|x| = \dfrac{x}{|x|}\]
geerky42
  • geerky42
on second thought, you was asked to estimate the derivative, but what we are doing is finding the actual derivative. hmm, not sure what to do here. do you have any idea?
geerky42
  • geerky42
what does "estimate the derivative" mean?
Issy14
  • Issy14
basically, when they ask us to do that they want an approximate value not the absolute value
geerky42
  • geerky42
huh, i am sorry, this problem confused me, because i don't see how chain rule can be apply to estimate value from given graph? so i am not sure... sorry.
Issy14
  • Issy14
it's ok, I'm confused as well, thank you for your help.
anonymous
  • anonymous
i think you are thinking too hard for this one
anonymous
  • anonymous
from the picture we see \(g(1)=3\) and \(g(3)=1\) so \(g(g(1))=g(3)=1\)
anonymous
  • anonymous
similarly \(g(2)=2\) so \(g(g(2))=g(2)=2\)
anonymous
  • anonymous
as for the derivative, \[\left(g(g(x)\right)'=g(g(x))g'(x)\] by the chain rule
anonymous
  • anonymous
ok that was a mistake!!
anonymous
  • anonymous
\[\left(g(g(x)\right)'=g'(g(x))g'(x)\]
anonymous
  • anonymous
then \[w'(1)=g'(g(1))\times g'(1)=-1\times -1=1\]
anonymous
  • anonymous
|dw:1404869501887:dw|
anonymous
  • anonymous
which should not surprise you since \(g(g(x))=x\)
Issy14
  • Issy14
then there was no need to find out the function of each one? I did that before but I thought that it was too simple. I will continue reading your answer, thank you. @satellite73 and @febylailani

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