Not the Second Derivative Test
Given that f is a function whose second derivative exists on an open interval I,
If f''(x) > 0 for all x in I, then the graph of f is concave up
If f''(x) < 0 for all x in I, then the graph of f is concave down
If f''(x) = 0 for all x in I, then the graph of f is linear
The Second Derivative Test
At a critical point (meaning derivative is 0 or und.) (x, f(x)),
If f''(x) < 0, x is a relative max
If f''(x) > 0, x is a relative min
If f''(x) = 0, it doesn't mean anything
David Witten