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SanjanaP
 2 years ago
Help with Increasing and Decreasing Derivatives Please!!
SanjanaP
 2 years ago
Help with Increasing and Decreasing Derivatives Please!!

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

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

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

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

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

myininaya
 2 years 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
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0I'm sorry..so what is g'?

myininaya
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0I'm not sure what differentiate means anymore?

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

myininaya
 2 years 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
 2 years 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
 2 years 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
 2 years 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
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0I would prefer the answer because I have to write the explanation anyway.

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

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

myininaya
 2 years 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
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0what about concave up?
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