Concavity Explorer
Explore how the second derivative determines concavity and inflection points
f(x) = x³ - 3x
f''(x) =
6x
Concavity:
changes at x=0
x³ - 3x
x⁴ - 2x²
sin(x)
f''(x) > 0 → concave up. f''(x) < 0 → concave down. f''(x) = 0 and changes sign → inflection point.