AP Calculus AB and BC glossary

Sign chart

Also called: Sign line, Sign diagram

A sign chart is a number line recording where a function or one of its derivatives is positive or negative. You mark the zeros and undefined points, test one value in each interval, and read off the signs to locate increasing and decreasing behavior and concavity.

The method is always the same. Find every value where the quantity is zero or undefined, mark those on a number line, pick a test point inside each open interval, and record the sign there. Signs of f′f' give increasing and decreasing; signs of f′′f'' give concave up and concave down.

One chart answers several questions at once. A single f′f' chart locates every local maximum and minimum by where the sign flips, and an f′′f'' chart locates every inflection point the same way.

The mistake

Turning in a bare sign chart as the justification on free response. Graders credit a sentence that names the sign change, such as f′f' changing from positive to negative at x=3x = 3. The chart is supporting work, not the argument itself.

Appears in: Unit 5: Analytical Applications