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myininaya Group TitleBest ResponseYou've already chosen the best response.1
compare to definition of derivative
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
\[\lim_{x \rightarrow a}\frac{f(x)f(a)}{xa}=f'(a)\]
 6 months ago

sam0004 Group TitleBest ResponseYou've already chosen the best response.0
So the limit would = 1?
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
what is f?
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
what is f(x) and what is a?
 6 months ago

sam0004 Group TitleBest ResponseYou've already chosen the best response.0
F(x)=sin(x), f(a)=sin(pi/6)
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
so what is f'?
 6 months ago

sam0004 Group TitleBest ResponseYou've already chosen the best response.0
Cos(x)cos(pi/6)?
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
:( if f=sin(x), then f'=?
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
right now plug in a to get your answer
 6 months ago

sam0004 Group TitleBest ResponseYou've already chosen the best response.0
A=sin(pi/6)?
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
\[\lim_{x \rightarrow a}\frac{f(x)f(a)}{xa}=f'(a) \text{ or we could say it equals } =(f(x))'_{x=a}\]
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
\[\lim_{x \rightarrow \frac{\pi}{6}}\frac{\sin(x)\sin(\frac{\pi}{6})}{x\frac{\pi}{6}}=(\sin(x))'_{x=\frac{\pi}{6}} \]
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
do you see all i'm trying to get you to do is use the definition of derivative
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
you are suppose to determine f and a then find f' then plug a into f' to get the result you are searching for
 6 months ago

sam0004 Group TitleBest ResponseYou've already chosen the best response.0
Sqrt(3)/2?
 6 months ago

sam0004 Group TitleBest ResponseYou've already chosen the best response.0
Any chance you can help with critical numbers?
 6 months ago

sam0004 Group TitleBest ResponseYou've already chosen the best response.0
F(x)=4x/x^2+1
 6 months ago

sam0004 Group TitleBest ResponseYou've already chosen the best response.0
I know i need the derivative
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
do you mean 4x/(x^2+1)? Also what did you get for the derivative?
 6 months ago

sam0004 Group TitleBest ResponseYou've already chosen the best response.0
Yes. F'(x)=(4x^2+4)/(x^2+1)^2
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
thats great now find when F'=0 Also we don't have to worry when F' DNE because x^2+1 is always positive. so F'=0 when top=0 so when 4x^2+4=0 solve for x now
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
I think you should retry solving 4x^2+4=0 I will give you a (you will get two real solutions)
 6 months ago

sam0004 Group TitleBest ResponseYou've already chosen the best response.0
...+orsqrt(1)
 6 months ago

sam0004 Group TitleBest ResponseYou've already chosen the best response.0
+orsqrt(1)
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
right sqrt(1)=1 so x=1 or x=1
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
those are the critical numbers for F.
 6 months ago

sam0004 Group TitleBest ResponseYou've already chosen the best response.0
Find the intervals where f(x)=4/(x^+1) is increasing or decreasing.
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
is that f(x)=4/(x+1)? like you weren't trying to write an exponent right?
 6 months ago

sam0004 Group TitleBest ResponseYou've already chosen the best response.0
I Find the derivative...then set the denominator equal to zero...put those numbers on a number line and plug in numbers to find the intervals?
 6 months ago

sam0004 Group TitleBest ResponseYou've already chosen the best response.0
I was writing an exponent
 6 months ago

sam0004 Group TitleBest ResponseYou've already chosen the best response.0
I apologize for missing the exponent
 6 months ago

sam0004 Group TitleBest ResponseYou've already chosen the best response.0
It should have said 4/(x^2+1)
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
well I don't know what f you are looking at exactly. but yeah you definitely need to find f' because f' tells you if f is decreasing or increasing or neither f'=0 means the function is resting f'>0 means f is increasing f'<0 means f is decreasing I first find when f' =0 and when f' does not exist and then test each interval around those numbers to see if the function is increasing there or decreasing there
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
so what is f' first?
 6 months ago

sam0004 Group TitleBest ResponseYou've already chosen the best response.0
8x/(x^4+1)
 6 months ago

sam0004 Group TitleBest ResponseYou've already chosen the best response.0
X=1 and x=1
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
(x^2+1)^2 does not equal x^4+1
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
just leave is at (x^2+1)^2
 6 months ago

sam0004 Group TitleBest ResponseYou've already chosen the best response.0
Increasing from negative infinity to 0 and decreasing from 0 to positive infinity
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
also x^2+1 is always positive so f' and f exist everywhere so you just need to find when f'=0 which is when 8x=0 which is when x=?
 6 months ago

sam0004 Group TitleBest ResponseYou've already chosen the best response.0
F(x)=3x^212x=5 over the closed interval 0,3. Find absolute extrema.
 6 months ago

sam0004 Group TitleBest ResponseYou've already chosen the best response.0
Do i again begin with taking the derivative?
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
see if there any critical numbers between 0 and 3 first
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
which means you need to find f' which all means you need find when f'=0 this looks like you meant to write a polynomial so we don't need to worry when f' dne
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
ok do F(0) and F(2) and F(3) which ever one of these are the lowest value is the absolute min value which ever one of these are the highest value is the absolute max value
 6 months ago

sam0004 Group TitleBest ResponseYou've already chosen the best response.0
Ok so you use the tow numbers in the interval and the critical number?
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
also I don't know what your function is exactly critical numbers in between the critical numbers and any included endpoints just plug them back into the original function
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
you have two equal signs
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
i'm guessing that second equal sign is a + or a 
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
can't decide which one
 6 months ago

sam0004 Group TitleBest ResponseYou've already chosen the best response.0
Should be +5
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
ok do you want me to check your answers for this one or are you just going through problems and getting ideas on how to do them so you can pass your final
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
like it seems like you are studying
 6 months ago

sam0004 Group TitleBest ResponseYou've already chosen the best response.0
I just need ideas on how to pass my final...i struggle with a few areas.
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
i would like to help you more but...
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
I have to go do some house stuff good luck on your final
 6 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
i hope i was helpful
 6 months ago
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