Math Playground
Calculus

Concave up & down

Cup-up or cup-down — and what the second derivative tells you.

A curve is concave up where it cups upward (like a smile) and concave down where it cups downward (like a frown).

Test

  • f''(x) > 0 — concave up.
  • f''(x) < 0 — concave down.
  • f''(x) = 0 — possible inflection point.