Question

inflection point of x^lnx

Answer 1

anyone please help!

Answer 2

do you know logarithmic differentiation?

Answer 3

yes

Answer 4

y = x^ln(x), then what?

Answer 5

(i found the first derivative which is (2lnx/x)x^lnx but then deriveing it again is trouble for me

Answer 6

product rule

Answer 7

but i did it a few times and got differnt answers

Answer 8

here is a formula
(fgh)' = f' gh + f g' h + fg h'

(2lnx/x)x^lnx = (2lnx) (1/x) x^ln(x)

derivative of that is:
(2/x) (1/x) x^ln(x) + (2lnx) (-1/x^2) x^ln(x) + (2lnx) (1/x) (2lnx) (1/x) x^ln(x)

now simplify

Answer 9

ok let me see if one of my answers the same

Answer 10

(2x^lnx) (1/x^2) (2ln^2(x) - ln(x) + 1)

Answer 11

i got (x^lnx) (2-2lnx+4ln^2(x))/x^2

Answer 12

samething if you were to factor out 2

Answer 13

oh ok sorry! so now i solve for x when i set this to zero right

Answer 14

yes.

Answer 15

ok im sure im going to need help with this too please

Answer 16

its just that i make minor mistakes that have big affects

Answer 17

ok im stuck at where i divide by 2x^lnx
then have 1-lnx+2lnx^2=0

Answer 18

i got next -lnx+2lnx^v=-1
then im stuck

Answer 19

can you solve 2u^2 - u + 1 = 0?

Answer 20

oh yes so we will get two answers?

Answer 21

i don't know. What does the quadratic formula say?

Answer 22

i dont know how to do it with lns

Answer 23

i could set u=lnx but thedn?

Answer 24

ln(x) = u = 1 +/- sqrt(1 - 4(2)(1))
--------------------
2(2)

Answer 25

the determinant is negative, thus, there is no solution.

So, f'(x) will never be equal to 0, so there is no inflection point

Answer 26

ohhhh oh

Answer 27

how to determine concavity then by looking at graph

Answer 28

since x > 0, plug in any positive number, say 1, in for x in f''(x) and see what the sign is.

f''(x) > 0 means concave up. Otherwise, concave down

Answer 29

its concave up

Answer 30

ok

Answer 31

can you help me with anothere one please

Answer 32

nope

Answer 33

y

Answer 34

tired

Answer 35

of what

Answer 36

can i ask you a general question please

Answer 37

not about math just random

Answer 38

ok

Answer 39

why do you help people online, with math stuff?

Answer 40

for fun

Answer 41

oh ok! where do you live? i sound like a creep but i promise its just curiosity lol

Answer 42

Arizona, US

Answer 43

OMG wow im in california, are you a girl?

Answer 44

no a guy

Answer 45

ok im a girl aha

Answer 46

cool

Answer 47

are u in college?

Answer 48

hey i see you helping others thts not fair!! ahah joking thanks for ur help!