a. Show that if the position x of a moving point is given by a quadratic function of t, x = At2 + Bt + C, then the average velocity over any time interval [t1, t2] is equal to the instan-taneous velocity at the midpoint of the time interval. b. What is the geometric significance of the result in part (a)?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.7: More On Inequalities
Problem 44E
icon
Related questions
Question

a. Show that if the position x of a moving point is given by a quadratic function of t, x = At2 + Bt + C, then the average velocity over any time interval [t1, t2] is equal to the instan-taneous velocity at the midpoint of the time interval.

b. What is the geometric significance of the result in part (a)?

Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 4 images

Blurred answer
Knowledge Booster
Implicit Differentiation
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage