AP Calculus AB and BC glossary
Linear approximation
Also called: Tangent line approximation
Linear approximation estimates a function near a point by using its tangent line there. It is accurate close to the point of tangency and degrades as you move away, and concavity tells you the direction of the error.
Concavity decides whether the estimate is too big or too small. Where the graph is concave up the tangent line lies below the curve, so the approximation underestimates; concave down overestimates.
The mistake
Claiming an over or underestimate without citing concavity. The justification has to name the sign of the second derivative on the relevant interval.
Appears in: Unit 4: Contextual Applications