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anonymous
 one year ago
If f(x) = 3a4x – 4 – ax, where a is some constant, find f ′(1).
Please help me guys, I give medals @preethat @phi
anonymous
 one year ago
If f(x) = 3a4x – 4 – ax, where a is some constant, find f ′(1). Please help me guys, I give medals @preethat @phi

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@phi could you help me

freckles
 one year ago
Best ResponseYou've already chosen the best response.0I remember this question and there was something fishy about it.. if a=0 then f(x)=0 then f'(x)=0 and so f'(1)=0 but what if a is not 0 then we have to consider 4x4>0 and 4x4<0 if 4x4>0 then x1>0 and then so f(x)=3a(4)(x1)ax if x>1 find f' for this side and if 4x4<0 then x1<0 and then so f(x)=3a(4)(x1)ax if x<1 find f' for this one see if f'(1) matches for both sides

phi
 one year ago
Best ResponseYou've already chosen the best response.0the derivative of  f(x)  is f(x) f'(x)/f(x)

freckles
 one year ago
Best ResponseYou've already chosen the best response.0I say it was fishy because of the choices that came with this problem

freckles
 one year ago
Best ResponseYou've already chosen the best response.0something about A) 1 B) 0 C) 1 D) can't remember

freckles
 one year ago
Best ResponseYou've already chosen the best response.0I don't know if those were the choices actually

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah, but could you explain me what they are actually asking, I mean I not want just the answer i was to know how to get answer because I really want to pass this exam

freckles
 one year ago
Best ResponseYou've already chosen the best response.0they are asking for f'(1)

freckles
 one year ago
Best ResponseYou've already chosen the best response.0I broken into a piecewise function

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so that means that first I have to find the derivate function and then plug 1?

freckles
 one year ago
Best ResponseYou've already chosen the best response.0@phi gave you something where you don't need piecewise function

phi
 one year ago
Best ResponseYou've already chosen the best response.0f(x) = 3a4x – 4 – ax, or f(x)= 12a  x 1 ax the derivative is 12 a (x1)/ x1  a

freckles
 one year ago
Best ResponseYou've already chosen the best response.0hopefully the a is not zero right it should really specify that the constant is not zero

phi
 one year ago
Best ResponseYou've already chosen the best response.0notice at x=1 we have an undefined quantity and the best we can do is write a limit, which is different for 1 and 1+

freckles
 one year ago
Best ResponseYou've already chosen the best response.0well that already says f' doesn't exist at x=1 we don't have to do the limit thing

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0those are the only options, but I am not sure whether to pick 1 or not enough 0 not enough information e 1

freckles
 one year ago
Best ResponseYou've already chosen the best response.0I would say not enough info because we don't know if a is 0 or not

freckles
 one year ago
Best ResponseYou've already chosen the best response.0like phi just show the f'(1) doesn't exist when a isn't 0 but when a=0 ,f(x)=0 and so f'(x)=0 and so f'(1)=0

freckles
 one year ago
Best ResponseYou've already chosen the best response.0you get two difference answers for two difference cases of a

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0true, I will select it and I'll see if the answer is correct, @phi said something similar, but i don't think they gave me enough information to solve the problem

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is that a modulus or a bracket?

freckles
 one year ago
Best ResponseYou've already chosen the best response.0if you want me to explain the piecewise function more I can by the way @Joseluess

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes please, I am a little confused

freckles
 one year ago
Best ResponseYou've already chosen the best response.0\[x=\left[\begin{matrix}x & \text{ if } x>0 \\ x & \text{ if } x<0 \\ 0 & \text{ if } x=0\end{matrix}\right]\] sorry don't know how to type a pretty piecewise function had to use the matrix code have you ever seen this and do you understand this?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes I know what you're talking about

freckles
 one year ago
Best ResponseYou've already chosen the best response.02=(2) I used row 2 since x=2<0 2=2 I used row 1 since x=2>0 0=0 used row 3 since x=0 anyways just in case you didn't know that now I could replace all those x's with any function and solve any resulting inequalities that occur for example I see we have 4x4 so I'm going to replace all the x's with (4x4)'s

freckles
 one year ago
Best ResponseYou've already chosen the best response.0\[4x4=\left[\begin{matrix}4x4 & \text{ if } 4x4>0 \\ (4x4) & \text{ if } 4x4<0 \\ 0 & \text{ if } 4x4=0\end{matrix}\right]\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.0now straightening this up a bit \[4x4=\left[\begin{matrix}4x4 & \text{ if } x>1 \\ (4x4) & \text{ if } x<1 \\ 0 & \text{ if } x=1\end{matrix}\right] \]

freckles
 one year ago
Best ResponseYou've already chosen the best response.0but when x>1 what is the derivative of 4x4 aka 4x4 since 4x4=4x4 for when x>1

freckles
 one year ago
Best ResponseYou've already chosen the best response.0\[(4x4)'=\left[\begin{matrix}(4x4)' & \text{ if } x>1 \\ (4x4)' & \text{ if } x<1 \\ ? & \text{ if } x=1\end{matrix}\right] \\ =...\] I left that one thing as a ? because we have to see if left derivative=right derivative (as x approaches 1 from both sides)

freckles
 one year ago
Best ResponseYou've already chosen the best response.0\[(4x4)'=\left[\begin{matrix}(4x4)' & \text{ if } x>1 \\ (4x4)' & \text{ if } x<1 \\ ? & \text{ if } x=1\end{matrix}\right] \\ (4x4)'=\left[\begin{matrix}4 & \text{ if } x>1 \\ 4 & \text{ if } x<1 \\ \text{ does not exist (since*)} & \text{ if } x=1\end{matrix}\right] \\ \\ \text{ since } f'(1^+) \ \neq f'(1^) \\ \text{ that is } 4 \neq 4 \]

freckles
 one year ago
Best ResponseYou've already chosen the best response.0now this already tells you that your function f(x)=3a4x4ax if a isn't 0 that you have f'(1) doesn't exist because (4x4)' evaluated at x=1 doesn't exist but now if a=0 your function is f(x)=3(0)4x40x=00=0 your function is f(x)=0 and so f'(x)=0 since derivative of a constant is 0 now f'(x)=0 does say it doesn't matter what x we have the f' value will always be 0 so f'(1)=0 if a=0

freckles
 one year ago
Best ResponseYou've already chosen the best response.0so summary of it all f'(1) can be 0 or doesn't exist

freckles
 one year ago
Best ResponseYou've already chosen the best response.0the information that doesn't allow us to say which is all dependent on what a is

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, so that's why the answer it not enough right? okay I understand it better thanks
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