hba
Checking my answers
if f(x)=x^39x^2+15x+3
What is the relative maxima ?



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hba
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I got 10.

waterineyes
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Really??

hba
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Yeah really.

waterineyes
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It will be right as it is calculated by the Great @hba
ha ha ha..

hba
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Thanks.

hba
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I have more question to get checked can i ask here or in a new post.

waterineyes
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I don't know how to solve these types of questions..
Can you teach me how to solve it..??

hba
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@waterineyes
Ha Ha Ha Nice joke,first let me ask my questions.

waterineyes
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First, we will take derivative..
Right??

hba
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Yeah.

waterineyes
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So wait, I am doing it..

hba
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okay :(

waterineyes
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f'(x) = 3x^2  18x + 15

sirm3d
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there are two extrema, 1 relative maximum and 1 relative minimum.

waterineyes
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Should I factorize it??

hba
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put f'(x)=0

waterineyes
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Yes I mean the same..

hba
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Then the answer is yes

waterineyes
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1
\[x^2  6x + 5 = 0 \implies (x  5)(x  1) = 0\]

waterineyes
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x = 5 and x = 1

hba
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Yes you are right

hba
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Now put 1 in the orignal equation.

waterineyes
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Why not 5 ??

hba
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Because we are finding the relative maxima

waterineyes
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f(1) = 10

sirm3d
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oooh, i misread the problem. relative maxima.

hba
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Correct.

waterineyes
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So, we have to put smaller value??

hba
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Yes.

waterineyes
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Just checking your answer..
Ha ha ha..

waterineyes
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Now don't say, to find relative minima, we will put 5..

hba
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dw:1355817149046:dw

hba
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@waterineyes Check these two questions.

waterineyes
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How to solve these now??

hba
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I got f'(x)=e in both the cases.

hba
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And f''(x)=1/e
for 1st
and
f''(x)=e
in the 2nd one.

hba
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So i am right ?

waterineyes
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Are you sure it is e ??

hba
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Pretty sure
Because i did this one like 100 times when i was in High school

waterineyes
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You have used division rule here??

hba
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U/V form.

waterineyes
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For first :
\[f'(x) = \frac{1  \ln(x)}{x^2}\]

hba
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Wait lemme check.

waterineyes
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Take your time..

hba
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Yeah right

hba
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@waterineyes ?

waterineyes
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Who is right??

hba
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The most intelligent @waterineyes

waterineyes
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Not intelligent as you @hba

waterineyes
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Now, find the second derivative..

hba
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Ha Ha Ha
Yeah wait.

hba
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I am getting something,which looks extremly wrong :/

hba
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@waterineyes
Here you go
\[f''(x)=x2x+2lnx/x^4\]
I kow it's wrong :/

waterineyes
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Sorry busy helping other person..

waterineyes
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Now I think, if it was e then it will be simpler..

waterineyes
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Wait, let me check..

hba
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ok

waterineyes
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You can add first two terms in the numerator..

hba
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Yeah i can add them so,
\[f''(x)=3x+2lnx/x^2\]

hba
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@waterineyes So ?

hba
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@waterineyes
Ansoo kahan ho tum ?

hba
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@waterineyes
Answer tau sahi hai mera,Is ki working mushkil hai :/

waterineyes
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Now what to do next??

waterineyes
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I had a guest in home so busy there..
Sorry, let us now work together..

waterineyes
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There??

hba
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yeah

hba
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@waterineyes Where should i continue ?

waterineyes
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What we will do next after finding second derivative??
To find extreme value..

hba
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put it equal to 0

waterineyes
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\[2 \ln(x) = 3x\]

waterineyes
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Where are we going??
Is that right??

hba
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i think we should skip these lol,I am pretty sure about my answers :)
Do you know what is a stationary point ?

waterineyes
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The point which is stationary is called Stationary Point, that's it..!!!

hba
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So,
if f(x)=ln(1+x^2)
What will be the stationary point ?

waterineyes
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I think I should go now..
Ha ha ha..
Seriously, don't know..

hba
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Gurpreet :/
Chalo Bye.