MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
A particle moves along a straight line, and its displacement x varies continuously with time t.
(i) Explain, with reasons, why the slope of the displacement–time graph at a particular instant represents the instantaneous velocity of the particle at that instant.
(ii) Starting from the definition of average velocity ΔtΔx, show algebraically that the instantaneous velocity v(t) can be written as v(t)=Δt→0limΔtΔx.