MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
A quantity y varies with x according to y=(x2+1)(x−3).
(i) Obtain dxdy using an appropriate rule.
(ii) Express the result from part (i) entirely in Lagrange notation f′(x), clearly identifying f(x).
(iii) Evaluate the derivative at x=3 in both notations.
(iv) If y represents distance (in metres) and x represents time (in seconds), interpret the numerical answer from part (iii) in physical terms.