Here's the question you clicked on:
burhan101
Determine the maximum and minimum. f(x)= 1+ (x+3)² ; -2<x<6
how does one find maxima and minima of a function?
first find the derivative f'(x)= 2x+6
sure it isnt \(-2 \le x\le 6\) ?
and what do we do with the derivative to find max and min (also known as critical points)?
f(-3)=1 f(-2)=2 f(6)=82
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)
yes i calculated it that way x=-3
and sorry i forgot to put \[-2 \le x \le 6\]
and you still don't know the answer?
you want the max and min values of the function; when is f(x) largest and smallest according to your calculations?
yes i get 6,82 as my max and -3,1 as my min BUT my answer key says maximum:82, minimum:6
Use the points you tested to find your highest and lowest values.
-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
@TuringTest so there a problem with the ansswerkey?
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.
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
so what would the local minimum be?
the local mina and max are also the global min and max in this case
\[\large f(x) = 1+(x+3)^2 \ \ , \ -2 \le x \le 6\]\[\large {f'(x) = 2(x+3)(1) =0 \\ f'(x)= 2x+6=0 }\]\[\large x = -3\] 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)
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
Sorry, Ab max = (6,82), Ab min = (-2,2) hehehe
well then we all agree :) nice job solving it though!
thanks! I typoed earlier :c
no worries, it happens to the best of us :P