**Question:** **True or False:** If \( f(t) \) is the distance of a particle from a fixed point after \( t \) units of time, then \( f'(t) \) is the instantaneous velocity of the particle after \( t \) units of time. **Explanation:** This statement involves understanding the relationship between a function and its derivative in calculus. Here, \( f(t) \) denotes the distance function, where \( t \) represents time. The derivative \( f'(t) \) gives the rate of change of the function \( f(t) \) at any specific moment \( t \). In this context, \( f'(t) \) represents the instantaneous velocity of the particle, as velocity is defined as the rate of change of distance with respect to time. Thus, the statement is **True**.

Question: True or False: If \( f(t) \) is the distance of a particle from a fixed point after \( t \) units of time, then \( f'(t) \) is the instantaneous velocity of the particle after \( t \) units of time. Explanation: This statement involves understanding the relationship between a function and its derivative in calculus. Here, \( f(t) \) denotes the distance function, where \( t \) represents time. The derivative \( f'(t) \) gives the rate of change of the function \( f(t) \) at any specific moment \( t \). In this context, \( f'(t) \) represents the instantaneous velocity of the particle, as velocity is defined as the rate of change of distance with respect to time. Thus, the statement is True.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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