**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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**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**.
Transcribed Image Text:**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**.
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