00:01
For this problem, we are asked to determine the intervals of constant concavity of the function f of x equals x over x squared plus 3, as well as to locate any inflection points.
00:11
Now, to begin with our analysis of the function here, what we'll have to do is first actually find the derivative, as well as the second derivative.
00:20
We can see that f prime of x, applying the quotient rule, f prime of x will be, after some simplification, 3 minus x squared, divided, by x squared plus 3 squared.
00:34
Differentiating again, we'll find that f double prime of x will be equal to negative 2x times 9 minus x squared, divided by x squared plus 3, all squared.
00:47
Or excuse me, not squared there, that would be cubed...