Question

y= (x^2-9)/(x^2+1)


find the max, min points and the inflection points

Answer 1

i first used the qoutient rule: which i got x^2(2x)(1-9)/9x^2-1)^2 WHATS NEXT?

Answer 2

simplified, my derivative came out to (20x)/(x^2+1)^2

Answer 3

ok but do i now equal that to 0 to find the min and max points?

Answer 4

for second derivative i got -20(3x^2-1)/(x^2+1)^3

Answer 5

set the first derivative to zero to find critical numbers.

Answer 6

so it should look like 20x/(x^2+1)^3=0

Answer 7

lemme double check...

Answer 8

yep...
http://www.wolframalpha.com/input/?i=derivative+of+%28x%5E2-9%29%2F%28x%5E2%2B1%29

Answer 9

do you want me to go over how that first derivative is obtained?

Answer 10

can u tell how to solve for the first max point?

Answer 11

paunic88: you want 20x/(x^2+1)^2=0

see dpaInc's derivative from above

Answer 12

ok so the max value is 1/3?

Answer 13

and the min is -1/3

Answer 14

no

Answer 15

set the derivative's numerator to zero which will give you 20x = 0 so x = 0. this is the x coodinate where your max/min will occur.

Answer 16

notice also that this function is defined for all real numbers so you don't have to worry about discontinuities

Answer 17

still there?