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anonymous
 4 years ago
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)
anonymous
 4 years ago
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)

This Question is Closed

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0start with finding expressions for u'(x) and v'(x)

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0u'(x)=f'(g(x))g'(x) v'(x)=g'(f(x))f'(x)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yeah i dont understand this. am i just looking at 3 on the graph?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0say 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?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0looks like g(3)=10 to me each square is 2 vertically, and 1 horizontally as far as I can tell

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0g(3)=8 I mean, sorry

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0I'm not really sure about the increments on the graph though, it's a bit vague...

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0It 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
 4 years ago
Best ResponseYou've already chosen the best response.0also remember that f'(4) represents the slope of f(x) at x=4

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0we 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
 4 years ago
Best ResponseYou've already chosen the best response.0when x is 4, f is 2 right?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0yes, 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?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0actually 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
 4 years ago
Best ResponseYou've already chosen the best response.0that 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
 4 years ago
Best ResponseYou've already chosen the best response.0rise over run right? 4/3? no?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0at x=3 it looks to me like g has a slope of 1

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0how did you figure that out?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0look 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
 4 years ago
Best ResponseYou've already chosen the best response.0here's a sketch of gdw:1329536578080:dw

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0here's the part from x=2 to x=4

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1329536693848:dwin your graph you can see it goes one over and one down on that region

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0(I'm not gonna draw the little squares in...)

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0so 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
 4 years ago
Best ResponseYou've already chosen the best response.0right, g(3)=4 and what is f'(g(3)) ?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0f is also 4 right? so that makes 4 x 4?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0no, we want f'(g(3))=f'(4) because g(3)=3, right ? what is f'(4) ?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0the slope of at 4 is 3

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0you are thinking about the idea correctly, but it looks like 2 to me

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok the gradients on this graph is crap

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0yeah, I agree with that, but the problem only seems to make sense if we count each square as 1...dw:1329537340258:dwso we want the slope of the upward portion of f

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0right, looks that way so what is u'(3)=f'(g(3))g'(3) ?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0there should be no 4 in the answer what is f'(g(3)) ?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0(we just figured it out above)

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0yes, and what is g'(3) ?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0so f'(g(3))g'(3) is what?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0u'(3)=f'(g(3))g'(3)=2 yep :D

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0so now you get to try for v'(3) ! good luck :)
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