Curve Sketching

thumbs137

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Oct 5, 2009
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So my math teacher gave us a quick little review on this today, but I can't even figure out the first question of my assignment.
I guess that my first question is, "what is the difference, or is there any, between extreme values, critical points, endpoints, and points of interest?"
The first question on my assignment is use the analytic method to fine extreme functions and where they occur for the function k(x)= e^-x^2. Do I need to take the derivative? My teacher said something about finding the domain, but I don't understand what that has to do with anything...

your help would definitely be appreciated!
~thumbs
 
f(x) = ex2, f  (x) = 2xex2\displaystyle f(x) \ = \ e^{-x^{2}}, \ f \ ' \ (x) \ = \ -2xe^{x^{2}}

Setting the slope = to 0, we get: 2xex2 = 0, x = 0, hence f(0) = 1 = max.\displaystyle Setting \ the \ slope \ = \ to \ 0, \ we \ get: \ -2xe^{x^{2}} \ = \ 0, \ x \ = \ 0, \ hence \ f(0) \ = \ 1 \ = \ max.

y = 0 is a horizontal asymptote and domain is (,), range is (0,1].\displaystyle y \ = \ 0 \ is \ a \ horizontal \ asymptote \ and \ domain \ is \ (-\infty,\infty), \ range \ is \ (0,1].

Note: See graph below.\displaystyle Note: \ See \ graph \ below.

[attachment=0:47h65gdl]def.jpg[/attachment:47h65gdl]
 

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OK. Thanks. But why did I need to find the domain and range? Is it supposed to help me understand something? And what defines a extreme point? Is it just any point that is used to sketch the graph?
 
Hey pal I dont read peoples minds (yours or your Professor), I just showed you some of the\displaystyle Hey \ pal \ I \ don't \ read \ peoples' \ minds \ (your's \ or \ your \ Professor), \ I \ just \ showed \ you \ some \ of \ the

 properties of f(x).\displaystyle \ properties \ of \ f(x).
 
I know. thank you. I guess i'm just trying to understand why it works and what it means. thanks for you help though.
 
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