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Help with Increasing and Decreasing Derivatives Please!!

Mathematics
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what is the question exactly?
If f'>0, then f is increasing If f'<0, then f is decreasing
Oh...sorry I thought I had the attachment on

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Other answers:

I neeed help with C and D
so are you having problems with the part highlighted in yellow?
Basically...
ok then so you know that g' will tell us if g is decreasing or increasing right?
Yeah
so 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
f(x)+0.5
F(x)+c right?
no 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'
I'm sorry..so what is g'?
you have to differentiate g(x)=F(x)-F(0) to find g' can you do that?
I'm not sure what differentiate means anymore?
to find derivative
It's f'(x)-f'(0)
f'(x)(x) right?
I 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
oh....so the derivative of F(x) is f(x). Is that what you mean?
That is what I said
so do you know F(0) is a constant?
its 0.5
I think you are thinking of f(0) not F(0) f is given not F
yea?
Anyways 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)
So going back to \[g(x)=\int\limits_{0}^{x} f(t) dt \\ g(x)=F(x)-F(0)\] can you differentiate g now?
what that means is you will have to differentiate both sides (not just one side)
Can you just tell me where it is increasing and concave up...so I'll try to figure it out?
Try 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
I would prefer the answer because I have to write the explanation anyway.
Okay...so you g(x)= F(x)-F(0)
that means g'(x) = f(x)-0?
I'm not going to give just the answer. Sorry. But right g'=f so that means the picture given is g'
and you know if g'>0, then g is increasing and you know if g'<0, then g is decreasing
where 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 x-axis that is where g is decreasing
what about concave up?
|dw:1407794546041:dw|

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