Question

Find the point on the curve

Answer 1

\[y=\frac{ x }{ x ^{2}+1 }\] where \[\frac{ dy }{ dx }=0\] and sketch the graph of this curve.

Answer 2

have you graphed the curve yet?

Answer 3

@radar

Answer 4

do you know how to compute the derivative ?

Answer 5

i got x*arctan(x)+1/(x^2+1) but im not sure

Answer 6

nope.
use the formula for the derivative of a quotient \((f/g)'\). the answer is has no arctan in it.

Answer 7

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

Answer 8

right

Answer 9

what about point?

Answer 10

it says where "(f/g)' = 0" . you just computed (f/g)' . now solve the equation.

Answer 11

but i'll contradict the answer

Answer 12

x^2+1 cannot be equal zero

Answer 13

x cannot be +or -1

Answer 14

but, in the answer it is

Answer 15

the numerator is 1-x^2. not 1+x^2.

Answer 16

i'm about denominator

Answer 17

that is x^2+1 in squares

Answer 18

but you don't care about the denominator. \(\frac AB = 0 \iff A=0\).
you only have to solve for the numerator.

Answer 19

mmmmmmm
mhhmmmm
mhhhhhhhhhhhhhhhhhmmm
thanks :DD

Answer 20

the two points are x=±1.