Question

which of the following statements are true about the graph of y=ln(4+x^2)
a)it is symmetric on the y axis
b)it has a local minimum at x=0
c) it has inflection points at = +/- 2

Answer 1

hey show your work

Answer 2

what do u mean? I don't know how to solve it..

Answer 3

A graph is symmetric about y axis if `f(x) = f(-x)`

Answer 4

you may use that for part a

Answer 5

ok but how would i find that out with that function?

Answer 6

\(y = f(x) = \ln(4+x^2)\)

replace x by -x for f(-x) :
\(f(-x) = \ln(4+(-x)^2) = \ln(4+x^2) = f(x)\)

that means...

Answer 7

that it isn't symmetric on the y axis

Answer 8

think again

Answer 9

ohh that it is symmetrical

Answer 10

Yep! thats it for part a
see if you can work remaining parts using first/second derivatives

Answer 11

thanks but I'm not sure how to get the first and second derivative since there is an ln..

Answer 12

use the derivative of ln and chain rule

Answer 13

\[\dfrac{d}{dx}(\ln x) = \frac{1}{x}\]

Answer 14

problem is on the second derivative, it's gonna get nastay

Answer 15

ok probably not.. I accidentally left the ln :P/ but second derivative is quotient rule

Answer 16

wait why would i use the chain rule

Answer 17

hmm there's no exponents I don't see the point.. umm do you know how to take derivatives for ln?

Answer 18

basically it's 1/ whatever it is inside the ln x (derivative of ln)

so for example I have

ln(2x)=y
1/2x (2) = y'

Answer 19

which simplifies to 1/x = y'
second time you take the derivative.. quotient rule

Answer 20

you know I have no idea why I can do math maturely on here... but when I'm in the class with this one particular guy prof.. quick I can't get my mind to focus.

Answer 21

wait the derivative of ln is 1/x, and then the derivative of (4+x^2) is 2x so we're left with 1/x(2x) right ?

Answer 22

ummmmmmm that's just ln x default
we're given ln 4+x^2

yes the derivative is 2x but

for derivative of ln we need 1 / (original function ) x (derivative inside the original function)

1/(4+x^2) x (2x)

Answer 23

then it's quotient rule on that guy

f/g


gf'-fg' / g^2

Answer 24

oh ok i see. so i must take the second derivative?

Answer 25

if we want to know concavity .. ?

hmm it's not asking that

just what interval are we in?

Answer 26

no it's just asking to know what is true about the graph. i have the answer choices on the question.

Answer 27

it could be all of them or 2 of them or only one..