The following items concern the idea of rate of change for a differentiable function.
MATHEMATICS · Multi-part · CBSE · Mathematics · Limits and Derivatives · Limits and Derivatives
Problem
The following items concern the idea of rate of change for a differentiable function.
(i) State the definition of the derivative of a real-valued function y=f(x) at a point x=a.
(ii) Distinguish between the average rate of change of f over an interval [a,a+h] and the instantaneous rate of change at x=a.
(iii) For the displacement function s(t)=3t2−2t+1, write the algebraic limit expression that represents the instantaneous velocity at a general time t; do not evaluate the limit.
(iv) Explain what information about the motion of the particle can be inferred when the derivative obtained in part (iii) is positive for t>0.