# 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