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CapO
United States1615 Posts
f(x) = te^(-t) by showing its critical points, intervals of increasing and decreasing, concavity and inflection points. ----------------------------------------------------- so far i have (t)'e^(-t) + (e^(-t))'t = 0 e^(-t) - e^(-t)(t) = 0 e^(-t)(1-t) = 0 t = 1 i don't know how to do e^(-t) = 0. ppl in my dorm don't know how to solve this, so please help.  | ||
mikeymoo
Canada7170 Posts
b/c e^-infinity = 1/e^infinity = 1/very big number --> 0. | ||
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CapO
United States1615 Posts
so i only test two points for increasing and decreasing? | ||
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Zortch
Canada635 Posts
f '(t)=(t-1)e^-t So, critical point is t=1 as you said. So look at f '(t) on (-infinity, 1) It is clearly always positive since 1-t>0 and e^-t>0 for all t. Thus, f is increasing on that interval. On (1, infinity) 1-t<0 so f is decreasing. Then for convavity, look at f ''(t) the second derivative. f ''(t)=(t-2)e^-t So, it is negative on (-infinity, 2) so f is concave down on that interval it is positive on (2, infinity) so f is concave up on that interval There is an inflection point at 2 since f ''(2)=0 So to sketch it, observe that as t goes to -infinity, f(t) goes to -infinity, and as t goes to infinity, f(t) goes to 0 Hopefully you can sketch it from here, if not I can upload something...or something. EDIT: I had my concavities mixed up, sry. | ||
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CapO
United States1615 Posts
edit : thank you mikeymoo! | ||
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Zortch
Canada635 Posts
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Ancestral
United States3230 Posts
@Op, good luck, study hard, persevere! And always go to tutor room / professor's office hours etc. | ||
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CapO
United States1615 Posts
On April 10 2008 14:48 Ancestral wrote: I have an integral calculus exam tomorrow. Luckily, I hear the farther you go in engineering, the less you have to deal with ridiculous abstract math. I like ridiculous abstract math, but not when I'm being graded on it. @Op, good luck, study hard, persevere! And always go to tutor room / professor's office hours etc. yup i have an exam on friday. wish me luck =/ | ||
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