Question

f(x) = xe^3/x

a) Use l'Hospital's Rule to determine the limit as x 0+.

b)Use calculus to find the local minimum value.

c)Find the interval where the function is concave up.

d) Find the interval where the function is concave down.

Answer 1

Yay right up my alley, love calculus!

Answer 2

wait is it f(x) = x * e^(3/x)?

Answer 3

yes

Answer 4

okay so rewrite that as:
f(x) = e^(3/x)/ (1/x)

Answer 5

according to l'hopitals the limit of that as it goes to 0, is:
(e^(3x^-1))'/(x^-1)'

Answer 6

hold on.. actually can we go on twiddla?

Answer 7

http://www.twiddla.com/578019
Go there it's easier for me to write.

Answer 8

As I showed u on twiddla the limit diverges.

Answer 9

Here's the picture..

Answer 10

what is diverges

Answer 11

Does not exist = goes to infinity, answer is inifinity techincally..

Answer 12

f(x) = xe^3/x
2) Use calc to find the local min:
that simply means taking the derivative:
f'(x) = x*e^(3/x) oh god I hate it when there's a variable in the power.. go back to that twiddla.. this will be messy.

Answer 13

that wasnt right for the limit

Answer 14

From the plus side? yes it was, and wolframalpha confirms it. Otherwise your question is wrong.

Answer 15

http://www.wolframalpha.com/input/?i=limit+%28xe%5E%283%2Fx%29%2Cx%2C0%29

Answer 16

no it wasnt right

Answer 17

im putting it into my online homework it said its wrong

Answer 18

can't be true, check the question then. Look wolframalpha is always true.

Answer 19

okay can i see a screen of ur online hw?

Answer 20

Try undefined, undef, DNE, infinity, infinity symbol, etc..

Answer 21

f(x) = x*e^(3/x)

Answer 22

infinity was right

Answer 23

how do i do the others?

Answer 24

okay let's go back to twiddla..

Answer 25

u are confusing me!

Answer 26

try x = 3 or x = 0, im too bored to check which one is max and which one is min.

Answer 27

did we get it?

Answer 28

nope

Answer 29

http://www.wolframalpha.com/input/?i=lim+x*e^(3%2Fx)%2Cx%2C0

Answer 30

what is that showing

Answer 31

The actual limits. It doesn't show you how to work them out.

Answer 32

yes but it doent show the minimum or concave up or down