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(Not) The Second Derivative Test

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

OIGOIG

Implicit Differentiation