Maximum and Minimum Problems (VCE SSCE Mathematical Methods): Flashcards

Finding best outcome by making a quantity max or min

Making a quantity as large as possible

Making a quantity as small as possible

Points where the derivative equals zero

Set derivative equal to zero and solve

Determine if stationary point is max, min, or neither

$f''(x) > 0$, gradient increasing, cup shape

$f''(x) < 0$, gradient decreasing, cap shape

Where curve changes concavity and $f''(x) = 0$

Both stationary points AND boundary values