How do you know where the graph of f(x) is concave up and where it is concave down for f(x) = x^3 + xf(x)=x3+x?

1 Answer
Aug 14, 2015

The graph of ff is concave up on intervals on which f''(x) is positive and the graph is concave down where f''(x) is negative.

Explanation:

So we need to investigate the sign of f''(x).

f(x) = x^3 + x

f'(x) = 3x^2+1

f''(x) = 6x

Clearly, f''(x) = 6x is negative for x <0 and positive for x>0.

So the graph of f is concave down on (-oo,0) and it is concave up on (0,oo)