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SanjanaP
 10 months ago
Help with Increasing and Decreasing Derivatives Please!!
SanjanaP
 10 months ago
Help with Increasing and Decreasing Derivatives Please!!

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myininaya
 10 months ago
Best ResponseYou've already chosen the best response.1what is the question exactly?

myininaya
 10 months ago
Best ResponseYou've already chosen the best response.1If f'>0, then f is increasing If f'<0, then f is decreasing

SanjanaP
 10 months ago
Best ResponseYou've already chosen the best response.0Oh...sorry I thought I had the attachment on

SanjanaP
 10 months ago
Best ResponseYou've already chosen the best response.0I neeed help with C and D

myininaya
 10 months ago
Best ResponseYou've already chosen the best response.1so are you having problems with the part highlighted in yellow?

myininaya
 10 months ago
Best ResponseYou've already chosen the best response.1ok then so you know that g' will tell us if g is decreasing or increasing right?

myininaya
 10 months ago
Best ResponseYou've already chosen the best response.1so find g' given that: \[g(x)=\int\limits_{0}^{x} f(t) dt \] don't look at the picture yet just tell what g' is

myininaya
 10 months ago
Best ResponseYou've already chosen the best response.1no i'm sorry that isn't correct ok let's look at this... I will rewrite it a little... \[g(x)=F(x)F(0)\] where F'=f Now differentiate to find g'

SanjanaP
 10 months ago
Best ResponseYou've already chosen the best response.0I'm sorry..so what is g'?

myininaya
 10 months ago
Best ResponseYou've already chosen the best response.1you have to differentiate g(x)=F(x)F(0) to find g' can you do that?

SanjanaP
 10 months ago
Best ResponseYou've already chosen the best response.0I'm not sure what differentiate means anymore?

myininaya
 10 months ago
Best ResponseYou've already chosen the best response.1I will help you out some more. derivative of g is g' derivative of F is f (this was given above when I said F'=f) derivative of a constant is 0 everything i said in this little post right here will need to be used

SanjanaP
 10 months ago
Best ResponseYou've already chosen the best response.0oh....so the derivative of F(x) is f(x). Is that what you mean?

myininaya
 10 months ago
Best ResponseYou've already chosen the best response.1That is what I said

myininaya
 10 months ago
Best ResponseYou've already chosen the best response.1so do you know F(0) is a constant?

myininaya
 10 months ago
Best ResponseYou've already chosen the best response.1I think you are thinking of f(0) not F(0) f is given not F

myininaya
 10 months ago
Best ResponseYou've already chosen the best response.1Anyways F(0) is a constant. Because F is a just a function of x any if you plug in a number for x then you will definitely receive a constant  example: Say F(x)=cos(x) well F(0) is definitely a constant because F(0) is 1 and 1 never changes (it is and will always remain 1)

myininaya
 10 months ago
Best ResponseYou've already chosen the best response.1So going back to \[g(x)=\int\limits_{0}^{x} f(t) dt \\ g(x)=F(x)F(0)\] can you differentiate g now?

myininaya
 10 months ago
Best ResponseYou've already chosen the best response.1what that means is you will have to differentiate both sides (not just one side)

SanjanaP
 10 months ago
Best ResponseYou've already chosen the best response.0Can you just tell me where it is increasing and concave up...so I'll try to figure it out?

myininaya
 10 months ago
Best ResponseYou've already chosen the best response.1Try to use what I said earlier... derivative of g is g' derivative of F' is f derivative of a constant is 0 you can do this

SanjanaP
 10 months ago
Best ResponseYou've already chosen the best response.0I would prefer the answer because I have to write the explanation anyway.

SanjanaP
 10 months ago
Best ResponseYou've already chosen the best response.0Okay...so you g(x)= F(x)F(0)

SanjanaP
 10 months ago
Best ResponseYou've already chosen the best response.0that means g'(x) = f(x)0?

myininaya
 10 months ago
Best ResponseYou've already chosen the best response.1I'm not going to give just the answer. Sorry. But right g'=f so that means the picture given is g'

myininaya
 10 months ago
Best ResponseYou've already chosen the best response.1and you know if g'>0, then g is increasing and you know if g'<0, then g is decreasing

myininaya
 10 months ago
Best ResponseYou've already chosen the best response.1where on the picture that is given is g' above the x axis (because that is where g is increasing) and when g' is below the xaxis that is where g is decreasing

SanjanaP
 10 months ago
Best ResponseYou've already chosen the best response.0what about concave up?

SanjanaP
 10 months ago
Best ResponseYou've already chosen the best response.0dw:1407794546041:dw
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