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burhan101
Group Title
Determine the maximum and minimum.
f(x)= 1+ (x+3)² ; 2<x<6
 one year ago
 one year ago
burhan101 Group Title
Determine the maximum and minimum. f(x)= 1+ (x+3)² ; 2<x<6
 one year ago
 one year ago

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TuringTest Group TitleBest ResponseYou've already chosen the best response.1
how does one find maxima and minima of a function?
 one year ago

burhan101 Group TitleBest ResponseYou've already chosen the best response.0
first find the derivative f'(x)= 2x+6
 one year ago

Jhannybean Group TitleBest ResponseYou've already chosen the best response.3
sure it isnt \(2 \le x\le 6\) ?
 one year ago

burhan101 Group TitleBest ResponseYou've already chosen the best response.0
yes @Jhannybean
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
and what do we do with the derivative to find max and min (also known as critical points)?
 one year ago

burhan101 Group TitleBest ResponseYou've already chosen the best response.0
f(3)=1 f(2)=2 f(6)=82
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
the critical points are found when the derivative is equal to zero (unless they are at the endpoints of the function, which you don;t need to worry about if you have no greater than or equal sign)
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
\(f'(x)\)=0
 one year ago

burhan101 Group TitleBest ResponseYou've already chosen the best response.0
yes i calculated it that way x=3
 one year ago

burhan101 Group TitleBest ResponseYou've already chosen the best response.0
and sorry i forgot to put \[2 \le x \le 6\]
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
and you still don't know the answer?
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
you want the max and min values of the function; when is f(x) largest and smallest according to your calculations?
 one year ago

burhan101 Group TitleBest ResponseYou've already chosen the best response.0
yes i get 6,82 as my max and 3,1 as my min BUT my answer key says maximum:82, minimum:6
 one year ago

Jhannybean Group TitleBest ResponseYou've already chosen the best response.3
Use the points you tested to find your highest and lowest values.
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
3 is not an option for x, but that leaves x=2, which still does not give 6... so I still do not see how that can be right
 one year ago

burhan101 Group TitleBest ResponseYou've already chosen the best response.0
@TuringTest so there a problem with the ansswerkey?
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
It's the only thing I see possible, and it certainly wouldn't be the first time I've seen the answer key be wrong.
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
http://www.wolframalpha.com/input/?i=plot+f%28x%29%3D+1%2B+%28x%2B3%29%C2%B2+%3B+2%3Cx%3C6 how 6 is a minimum in this graph is beyond me
 one year ago

burhan101 Group TitleBest ResponseYou've already chosen the best response.0
so what would the local minimum be?
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
the local mina and max are also the global min and max in this case
 one year ago

Jhannybean Group TitleBest ResponseYou've already chosen the best response.3
\[\large f(x) = 1+(x+3)^2 \ \ , \ 2 \le x \le 6\]\[\large {f'(x) = 2(x+3)(1) =0 \\ f'(x)= 2x+6=0 }\]\[\large x = 3\] Test your end points and your critical points with the help of The Extreme Value Theorem. 1. your function is continuous since it's a polynomial 2. x=3 does not fall between the interval [2,6] so cannot be tested. 3.Test your end points \[\large {f(2) = 1+((2)+3)^2 = 2 }\]\[\large f(6) = 1+ ((6)+3)^2= 82\] Ab max = (2,2) Ab Min = (6,82)
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
I agree, and think the answer key is wrong. I would guess it a typo where someone wrote the x=6 which corresponds to the max instead of the min. It really is not that uncommon; books can be mistaken :p
 one year ago

Jhannybean Group TitleBest ResponseYou've already chosen the best response.3
Sorry, Ab max = (6,82), Ab min = (2,2) hehehe
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
well then we all agree :) nice job solving it though!
 one year ago

Jhannybean Group TitleBest ResponseYou've already chosen the best response.3
thanks! I typoed earlier :c
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
no worries, it happens to the best of us :P
 one year ago
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