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Answer 1 · 2017-04-08T21:13:51

Please see below.

#y = (6x)/(x^2+3)#

The domain is #RR#

#y' = (-6(x^2-3))/(x^2+3)#

#y''=(12x(x^2-9))/(x^2+3)^3#

#y'' = 0# at #x = 0#, #3# and #-3#.

The denominator of #y''# is always positive and the numerator changes sign at each of its three zeros.

Therefore, #y''# changes sign 3 times.