Help with Increasing and Decreasing Derivatives Please!!

- SanjanaP

Help with Increasing and Decreasing Derivatives Please!!

- jamiebookeater

See more answers at brainly.com

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- myininaya

what is the question exactly?

- myininaya

If f'>0, then f is increasing
If f'<0, then f is decreasing

- SanjanaP

Oh...sorry I thought I had the attachment on

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- SanjanaP

I neeed help with C and D

##### 1 Attachment

- SanjanaP

@myininaya

- myininaya

so are you having problems with the part highlighted in yellow?

- SanjanaP

Basically...

- myininaya

ok then so you know that g' will tell us if g is decreasing or increasing right?

- SanjanaP

Yeah

- 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

f(x)+0.5

- SanjanaP

F(x)+c right?

- 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

I'm sorry..so what is g'?

- myininaya

you have to differentiate g(x)=F(x)-F(0) to find g'
can you do that?

- SanjanaP

I'm not sure what differentiate means anymore?

- myininaya

to find derivative

- SanjanaP

It's f'(x)-f'(0)

- SanjanaP

f'(x)(x) right?

- 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

oh....so the derivative of F(x) is f(x). Is that what you mean?

- myininaya

That is what I said

- myininaya

so do you know F(0) is a constant?

- SanjanaP

its 0.5

- myininaya

I think you are thinking of f(0) not F(0)
f is given not F

- SanjanaP

yea?

- 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

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

what that means is you will have to differentiate both sides (not just one side)

- SanjanaP

Can you just tell me where it is increasing and concave up...so I'll try to figure it out?

- 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

I would prefer the answer because I have to write the explanation
anyway.

- SanjanaP

Okay...so you g(x)= F(x)-F(0)

- SanjanaP

that means g'(x) = f(x)-0?

- myininaya

I'm not going to give just the answer. Sorry.
But right g'=f
so that means the picture given is g'

- myininaya

and you know if g'>0, then g is increasing
and you know if g'<0, then g is decreasing

- 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

what about concave up?

- SanjanaP

|dw:1407794546041:dw|

Looking for something else?

Not the answer you are looking for? Search for more explanations.