SanjanaP
  • SanjanaP
Help with Increasing and Decreasing Derivatives Please!!
Mathematics
jamiebookeater
  • jamiebookeater
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myininaya
  • myininaya
what is the question exactly?
myininaya
  • myininaya
If f'>0, then f is increasing If f'<0, then f is decreasing
SanjanaP
  • SanjanaP
Oh...sorry I thought I had the attachment on

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SanjanaP
  • SanjanaP
I neeed help with C and D
SanjanaP
  • SanjanaP
@myininaya
myininaya
  • myininaya
so are you having problems with the part highlighted in yellow?
SanjanaP
  • SanjanaP
Basically...
myininaya
  • myininaya
ok then so you know that g' will tell us if g is decreasing or increasing right?
SanjanaP
  • SanjanaP
Yeah
myininaya
  • myininaya
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
SanjanaP
  • SanjanaP
f(x)+0.5
SanjanaP
  • SanjanaP
F(x)+c right?
myininaya
  • myininaya
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'
SanjanaP
  • SanjanaP
I'm sorry..so what is g'?
myininaya
  • myininaya
you have to differentiate g(x)=F(x)-F(0) to find g' can you do that?
SanjanaP
  • SanjanaP
I'm not sure what differentiate means anymore?
myininaya
  • myininaya
to find derivative
SanjanaP
  • SanjanaP
It's f'(x)-f'(0)
SanjanaP
  • SanjanaP
f'(x)(x) right?
myininaya
  • myininaya
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
SanjanaP
  • SanjanaP
oh....so the derivative of F(x) is f(x). Is that what you mean?
myininaya
  • myininaya
That is what I said
myininaya
  • myininaya
so do you know F(0) is a constant?
SanjanaP
  • SanjanaP
its 0.5
myininaya
  • myininaya
I think you are thinking of f(0) not F(0) f is given not F
SanjanaP
  • SanjanaP
yea?
myininaya
  • myininaya
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)
myininaya
  • myininaya
So going back to \[g(x)=\int\limits_{0}^{x} f(t) dt \\ g(x)=F(x)-F(0)\] can you differentiate g now?
myininaya
  • myininaya
what that means is you will have to differentiate both sides (not just one side)
SanjanaP
  • SanjanaP
Can you just tell me where it is increasing and concave up...so I'll try to figure it out?
myininaya
  • myininaya
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
SanjanaP
  • SanjanaP
I would prefer the answer because I have to write the explanation anyway.
SanjanaP
  • SanjanaP
Okay...so you g(x)= F(x)-F(0)
SanjanaP
  • SanjanaP
that means g'(x) = f(x)-0?
myininaya
  • myininaya
I'm not going to give just the answer. Sorry. But right g'=f so that means the picture given is g'
myininaya
  • myininaya
and you know if g'>0, then g is increasing and you know if g'<0, then g is decreasing
myininaya
  • myininaya
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
SanjanaP
  • SanjanaP
what about concave up?
SanjanaP
  • SanjanaP
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