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Matthew071
Group Title
Need help on differentiables. Determining the values of constants
 one year ago
 one year ago
Matthew071 Group Title
Need help on differentiables. Determining the values of constants
 one year ago
 one year ago

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Matthew071 Group TitleBest ResponseYou've already chosen the best response.0
\[f(x)=\left[\begin{matrix}6x^3 & x \le 1 \\ Bx+C & 1 < x\end{matrix}\right]\]
 one year ago

Matthew071 Group TitleBest ResponseYou've already chosen the best response.0
How do I find B and C
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.1
Take the derivative of the function (each function separately), then make the derivative continuous.
 one year ago

Matthew071 Group TitleBest ResponseYou've already chosen the best response.0
Ok so i just take the derivitive of both: \[f'(x)=\left[\begin{matrix}18x^2 & x<=1 \\ B & 1<x\end{matrix}\right]\]
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.1
Now insert \(x=1\) for both parts, and solve for \(B\)
 one year ago

Matthew071 Group TitleBest ResponseYou've already chosen the best response.0
ok so: \[f'(x)=18(1)^2=18 = B\] Correct?
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.1
Now you need to make the original function continuous.
 one year ago

Matthew071 Group TitleBest ResponseYou've already chosen the best response.0
So: \[f(x)= 18(1)+C<1\]
 one year ago

Matthew071 Group TitleBest ResponseYou've already chosen the best response.0
So c=17?
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.1
No, the other equation to equal it to is \(6(1)^3\)
 one year ago

Matthew071 Group TitleBest ResponseYou've already chosen the best response.0
Oh ok so then f(x)=6 so then: \[18(1)+C=6\] Then I do this \[C=12\]
 one year ago

Matthew071 Group TitleBest ResponseYou've already chosen the best response.0
Correct?
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
C and B values are both correct. Looking over your work though, I'm not sure you understand what wio was trying to get you to do.
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
I'm saying your work could use a little work. :p But yes the answers are right.
 one year ago

Matthew071 Group TitleBest ResponseYou've already chosen the best response.0
Thats fine as long as your trying to help out :)
 one year ago

Matthew071 Group TitleBest ResponseYou've already chosen the best response.0
So when I see a problem like this I take the derivative of both equations and make the darivative continuous. Then I go back and plug in B and make just f(x) continous.
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Basically they were trying to make the function f continue and also trying to make the function f' continuous Make the function f' continuous will make the function f differential if we choose the right values for B and C of course. So when we looked at f We did the left and right limit as x approaches 1. Set both the left limit expression and the right limit expression equal. We notice here we don't have enough info to solve for B and C, but we do have an equation relating C and B from the left limit expression=right limit expression equation. f(x)=6x^3 f(x)=Bx+C __________________________________ 1 You want both sides of 1 to be equal as they approach 1. So left limit expression is 6(1)^3 and the right limit expression is B(1)+C Remember you need to set these equal giving you that relationship between B and C that was talking about. Now we also need to find f' f'(x)=18x^2 f'(x)=B  1 You do the same here that you did for the original function f. You set the left limit expression equal to the right limit expression as x approaches 1.
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
I'm just making sure you understand so you can tackle problems like this in the future.
 one year ago

Matthew071 Group TitleBest ResponseYou've already chosen the best response.0
Ya it makes much more sense now. Thank you myininaya!
 one year ago
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