Mathematical Methods · second derivative · manipulative

Which way does the curve bend?

Move x along the curve. Where f″ > 0 the tangent lies under the curve; where f″ < 0 it lies over it. The swap happens at a point of inflection.

y = f(x) tangent at x f″ > 0 f″ < 0 inflection

Drag the point on the curve · scroll zoom · drag background to pan

Point x

1.4

Show concavity
shade where f″ > 0 and f″ < 0

Working