MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
For the function r(x)=3x4−2x3+x2−5, the instantaneous rate of change at x=1 is required.
(a) Write the limit that represents r′(1).
(b) Evaluate this limit exactly to find r′(1).
(c) Using h=0.0001, compute the numerical difference quotient hr(1+h)−r(1) and compare it with the value obtained in part (b) correct to four decimal places.