anonymous
  • anonymous
If f and g are the functions whose graphs are shown below, let u(x)=f(g(x)) and v(x)=g(f(x)) . find u'(3) and v'(3)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
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TuringTest
  • TuringTest
start with finding expressions for u'(x) and v'(x)
TuringTest
  • TuringTest
u'(x)=f'(g(x))g'(x) v'(x)=g'(f(x))f'(x)

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More answers

anonymous
  • anonymous
yeah i dont understand this. am i just looking at 3 on the graph?
TuringTest
  • TuringTest
say you want u'(3), you first need g(3) because g(x) is part of the formula you need what is g(3) according to the graph?
anonymous
  • anonymous
looks like 4
TuringTest
  • TuringTest
looks like g(3)=10 to me each square is 2 vertically, and 1 horizontally as far as I can tell
TuringTest
  • TuringTest
g(3)=8 I mean, sorry
TuringTest
  • TuringTest
I'm not really sure about the increments on the graph though, it's a bit vague...
anonymous
  • anonymous
8, how so?
TuringTest
  • TuringTest
It looks to me like each square vertically is 2 (by the marking), but I guess it must be 4 since 8 is not on the graph horizontally so ok, g(3)=4 what is the value of f'(4) ? [remember we need f'(g(3))g'(3)]
TuringTest
  • TuringTest
also remember that f'(4) represents the slope of f(x) at x=4
anonymous
  • anonymous
f(4) is 2
TuringTest
  • TuringTest
we want f'(4) that is the slope of f(x) at x=4 what is the slope of the line in the graph f(x) at x=4 ?
anonymous
  • anonymous
when x is 4, f is 2 right?
TuringTest
  • TuringTest
yes, but that is the value of f(4) not f'(4) f'(4) is the SLOPE, not the value of the function do you remember how to find the slope of a straight line from algebra?
anonymous
  • anonymous
ohh
anonymous
  • anonymous
y2-y1/x2-x1?
TuringTest
  • TuringTest
actually sorry, they are the same in this case, but that is pure luck! lol notice that the slope (rise over run) is also 2 !
TuringTest
  • TuringTest
that is what f' means, the slope of f so similarly what is the last piece of the formula we need ? u'(3)=f'(g(3))g'(3) and we still need g'(3) what is it?
anonymous
  • anonymous
rise over run right? 4/3? no?
TuringTest
  • TuringTest
at x=3 it looks to me like g has a slope of -1
anonymous
  • anonymous
how did you figure that out?
TuringTest
  • TuringTest
look at the tail last portion of g(x), the far right portion of the top graph. it dips downward it seems to go down one unit for every unit it goes to the right rise/run=-1/1=-1
TuringTest
  • TuringTest
here's a sketch of g|dw:1329536578080:dw|
anonymous
  • anonymous
ok i see now i see
TuringTest
  • TuringTest
here's the part from x=2 to x=4
TuringTest
  • TuringTest
|dw:1329536693848:dw|in your graph you can see it goes one over and one down on that region
TuringTest
  • TuringTest
(I'm not gonna draw the little squares in...)
anonymous
  • anonymous
i see that thanks
TuringTest
  • TuringTest
so you have all the pieces now u'(3)=f'(g(3))g'(3) you know f'(g(3)) and g'(3), so multiply them to find u'(3)
TuringTest
  • TuringTest
what is g(3) ?
anonymous
  • anonymous
4 slope is -1
TuringTest
  • TuringTest
right, g(3)=4 and what is f'(g(3)) ?
anonymous
  • anonymous
f is also 4 right? so that makes 4 x 4?
TuringTest
  • TuringTest
no, we want f'(g(3))=f'(4) because g(3)=3, right ? what is f'(4) ?
anonymous
  • anonymous
the slope of at 4 is 3
TuringTest
  • TuringTest
you are thinking about the idea correctly, but it looks like 2 to me
anonymous
  • anonymous
ok the gradients on this graph is crap
TuringTest
  • TuringTest
yeah, I agree with that, but the problem only seems to make sense if we count each square as 1...|dw:1329537340258:dw|so we want the slope of the upward portion of f
anonymous
  • anonymous
4/2
anonymous
  • anonymous
2
TuringTest
  • TuringTest
right, looks that way so what is u'(3)=f'(g(3))g'(3) ?
anonymous
  • anonymous
(2)(4) (4)
TuringTest
  • TuringTest
there should be no 4 in the answer what is f'(g(3)) ?
TuringTest
  • TuringTest
(we just figured it out above)
anonymous
  • anonymous
2
TuringTest
  • TuringTest
yes, and what is g'(3) ?
anonymous
  • anonymous
-1
TuringTest
  • TuringTest
so f'(g(3))g'(3) is what?
anonymous
  • anonymous
(2) (-1)
TuringTest
  • TuringTest
u'(3)=f'(g(3))g'(3)=-2 yep :D
anonymous
  • anonymous
thanks for the help
TuringTest
  • TuringTest
so now you get to try for v'(3) ! good luck :)
anonymous
  • anonymous
I got zero
TuringTest
  • TuringTest
yep!

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