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Contextual Applications of Differentiation

Samuel Baker

Samuel Baker

4 min read

Study Guide Overview

This unit covers applying differentiation to real-world contexts, including motion, related rates, approximations, and L'Hôpital's Rule. It builds upon prerequisite knowledge of differentiation rules, derivatives of various functions, and basic formulas. The unit emphasizes understanding derivatives as instantaneous rates of change and applying them to scenarios like one-dimensional motion involving position, velocity, acceleration, and speed.

Previous Topic - Calculating Higher-Order DerivativesNext Topic - Interpreting the Meaning of the Derivative in Context

Question 1 of 3

🚗💨 If the position of a particle is given by x(t)=2t2+3t−1x(t) = 2t^2 + 3t - 1, what is the velocity function, v(t)v(t)?

v(t)=4t+3v(t) = 4t + 3

v(t)=t3+frac32t2−tv(t) = t^3 + frac{3}{2}t^2 - t

v(t)=2t+3v(t) = 2t + 3

v(t)=4t2+3v(t) = 4t^2 + 3