In a time of t seconds, a particle moves a distance of s meters from its starting point, where s(t) = 3t2 − 1. 1. Complete the following table of values. Do not round your solutions. t 2 2.001 2.01 2.1 s(t) 2. Find the average rate of change between t = 2 and t = 2 + ∆t if: i. ∆t = 0.1 ii. ∆t = 0.01 iii. ∆t = 0.001 3. As we choose a smaller and smaller interval around t = 2 the average rate of change appears to be getting closer and closer to the numerical value _____ . So we estimate the instantaneous rate of change at t = 2 to be _____ m/sec. 4. Find s'(t) using rules of differentiation. 5. Use s'(t) to find the exact value of s'(2)

In a time of t seconds, a particle moves a distance of s meters from its starting point, where s(t) = 3t2 − 1. 1. Complete the following table of values. Do not round your solutions. t 2 2.001 2.01 2.1 s(t) 2. Find the average rate of change between t = 2 and t = 2 + ∆t if: i. ∆t = 0.1 ii. ∆t = 0.01 iii. ∆t = 0.001 3. As we choose a smaller and smaller interval around t = 2 the average rate of change appears to be getting closer and closer to the numerical value _ . So we estimate the instantaneous rate of change at t = 2 to be _ m/sec. 4. Find s'(t) using rules of differentiation. 5. Use s'(t) to find the exact value of s'(2)

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section: Chapter Questions

Problem 33CT

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t	2	2.001	2.01	2.1
s(t)