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compare to definition of derivative

\[\lim_{x \rightarrow a}\frac{f(x)-f(a)}{x-a}=f'(a)\]

So the limit would = 1?

no

what is f?

...?

what is f(x) and what is a?

F(x)=sin(x), f(a)=sin(pi/6)

so what is f'?

Cos(x)-cos(pi/6)?

:(
if f=sin(x), then f'=?

Cos(x)

right
now plug in a to get your answer

A=sin(pi/6)?

do you see all i'm trying to get you to do is use the definition of derivative

Sqrt(3)/2?

yep

Thank you

Any chance you can help with critical numbers?

sure

F(x)=4x/x^2+1

I know i need the derivative

do you mean 4x/(x^2+1)?
Also what did you get for the derivative?

Yes.
F'(x)=(-4x^2+4)/(x^2+1)^2

Sqrt(-1)

I think you should retry solving -4x^2+4=0
I will give you a (you will get two real solutions)

...+or-sqrt(-1)

+or-sqrt(1)

right sqrt(1)=1
so x=1 or x=-1

those are the critical numbers for F.

Wow...

Find the intervals where f(x)=4/(x^+1) is increasing or decreasing.

is that f(x)=4/(x+1)?
like you weren't trying to write an exponent right?

I was writing an exponent

I apologize for missing the exponent

It should have said 4/(x^2+1)

so what is f' first?

-8x/(x^4+1)

X=-1 and x=1

(x^2+1)^2 does not equal x^4+1

just leave is at (x^2+1)^2

Increasing from negative infinity to 0 and decreasing from 0 to positive infinity

ok yep

F(x)=3x^2-12x=5 over the closed interval 0,3. Find absolute extrema.

Do i again begin with taking the derivative?

see if there any critical numbers between 0 and 3 first

X=2

Ok so you use the tow numbers in the interval and the critical number?

you have two equal signs

i'm guessing that second equal sign is a + or a -

can't decide which one

Should be +5

like it seems like you are studying

I just need ideas on how to pass my final...i struggle with a few areas.

i would like to help you more but...

I have to go do some house stuff
good luck on your final

i hope i was helpful

Ok thanks