Question

Determine where the given function is concave up or where it is concave down:

f(x)=9x/x^2+49

Answer 1

f = 9x/(x^2 + 49)

f is concave up where f'' > 0

f' = -9(x^2 - 49) / (x^2 + 49)^2

f'' = 18x(x^2 - 147)/(x^2 + 49)^3

f'' < 0 where 0 < x < √147 or x < -√147
f'' > 0 where -√147 < x < 0 or x > √147