AP Calculus AB and BC glossary
Decreasing function
A function is decreasing on an interval when larger inputs give smaller outputs. On an interval where the function is differentiable, this happens exactly when the derivative is negative, and the endpoints of such intervals are where the derivative changes sign.
Answer with intervals of x-values, not with y-values or with points. On free response, an interval stated without justification from the sign of the derivative usually earns nothing.
The mistake
Confusing decreasing with concave down. A function can decrease while curving either way; concavity is a statement about the second derivative.
Appears in: Unit 5: Analytical Applications