\input zb-basic \input zb-matheduc \iteman{ZMATH 2010a.00525} \itemau{Smith-Risser, H.} \itemti{Exploring numerical derivatives.} \itemso{Math. Teach. (Reston) 102, No. 3, 224-230 (2008).} \itemab From the text: The purpose of the activity is not to discourage students from using their calculators. Instead, it is designed to teach them to use their conceptual understanding of derivatives to evaluate the reasonableness of their numerical answers. This activity can be introduced in Calculus AB or BC at any time after students understand the definition of the derivative and the relationship between slopes of secant lines and slopes of tangent lines. Although I used this activity after teaching many of the basic derivative rules, students need not know the derivative rules to complete the activity. Many examples used in the activity are chosen specifically because the numerical derivative produced is not a good approximation of the slope of the tangent line. \itemrv{~} \itemcc{N44 I44} \itemut{secants; tangents; worksheets; differential calculus; approximation; numerical differentiation; student activities} \itemli{} \end