Sketch from Signs CalcLens

You are not asked to plot points. On any stretch where f′ and f″ keep their signs there are only four shapes a graph can have — pick one per interval and the sketch assembles itself.

Pick a shape, then click the interval it belongs to — or drag it there. The sign charts are under the graph, lined up with the axis.

The only four shapes

Sketch from Signs

On any interval where f′ and f″ both keep their signs, the graph can only do one of four things. Rising or falling is f′; bending up or down is f″. Two signs, four combinations, four shapes — and a curve sketch is those shapes laid end to end.

How to work it

  1. The cut points are already found for you: they are where f′ or f″ changes sign — the critical points and the inflection points.
  2. Read the two signs in a column.
  3. Pick the shape those two signs force.
  4. The heights are given, so each piece starts and ends where it must.
  5. Check my sketch marks each interval and lays the real graph over the top.

If a shape disagrees with the numbers

Saying "rising" on an interval that ends lower than it starts is a contradiction, and the tool says so specifically rather than just marking it wrong. That mismatch is the most common way a sketch goes astray: the shape and the values have to tell the same story.

Keyboard

R
Show or hide the real graph
?
This dialog
Esc
Close