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anonymous
 one year ago
Graph the function f(x)=x^3−2x and it's secant line through the points (2,4) and (2,4). Use the graph to estimate the xcoordinate of the points where the tangent line is parallel to the secant line.
Find the exact value of the numbers c that satisfy the conclusion of the mean value theorem for the interval [2,2].
anonymous
 one year ago
Graph the function f(x)=x^3−2x and it's secant line through the points (2,4) and (2,4). Use the graph to estimate the xcoordinate of the points where the tangent line is parallel to the secant line. Find the exact value of the numbers c that satisfy the conclusion of the mean value theorem for the interval [2,2].

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I need help finding 'c'

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I know that the Mean Value Theorem says... \[\frac{ f(b)f(a) }{ ba }=f'(c)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0But that gives me f'(c)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Right, plugging all that in do you get f'(c) = 2 ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0f(b)=2^32(2)..rite?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Doesn't it already give us the coordinates for the points? (2,4) and (2,4)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is it wrong to say \[\frac{ 4+4 }{ 2+2}=\frac{ 8 }{ 4 } = 2\] ? Or am I totally wrong right now? Lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what did u do just now?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3\[(x^32x)'_{x=c}=\frac{f(2)f(2)}{2(2)} \\ (x^32x)'_{x=c}=\frac{4(4)}{2(2)} \\ (x^32x)'_{x=c}=\frac{4+4}{2+2}\] that is right for the right hand side

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well I plugged in f(a) = 4, f(b) = 4, and a=2, b=2 in the mean value theorem formula

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what happens to the left hand side?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0do i just derive it?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3you still have to differentiate the left hand side and plug in c afterwards as the equation above suggests

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3yep and plug in c (though that part doesn't matter to much; it is just what they call it in the formula above) yep now solve 3x^22=2

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3or you named it c 3c^22=2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ohh so then its +/ 2/sqrt3 right?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3are both of those in the given interval?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3though there are two problems

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3did you do the first problem?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yay!!! Thats correct! :D Thank you so much!

myininaya
 one year ago
Best ResponseYou've already chosen the best response.3we did the second problem we found the exact solutions

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah Im always better in graphing haha

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thanks again for the help! :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0tracy?got the answer for the second part?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah! I got it, its + or  2/sqrt3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you too @chethus!
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