i never thought i'd ask, but help me with calc plz

CapO

United States1615 Posts

April 10 2008 04:04 GMT

1. (10pts) sketch the graph of the following function:

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

April 10 2008 04:09 GMT

e^(-t) will never equal zero. It will approach zero as t approaches infinity.
b/c e^-infinity = 1/e^infinity = 1/very big number --> 0.

CapO

United States1615 Posts

April 10 2008 04:10 GMT

|-----------1-----------|

so i only test two points for increasing and decreasing?

Zortch

Canada635 Posts

April 10 2008 04:18 GMT

f(x)=te^-t
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.

CapO

United States1615 Posts

April 10 2008 04:28 GMT

thanks a lot zortch. ur a life saver! =]

edit : thank you mikeymoo!

Zortch

Canada635 Posts

April 10 2008 04:30 GMT

Make sure you understand it or you'll get owned on the exam! xD

Ancestral

United States3230 Posts

April 10 2008 05:48 GMT

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.

CapO

United States1615 Posts

April 10 2008 05:50 GMT

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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i never thought i'd ask, but help me with calc plz

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