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
Find indicated rate of number 3

Transcribed Image Text:**Chapter 3.9 Exercise Set**
Find the indicated rate.
1. Given \( y = x^3 \), find \( \frac{dy}{dt} \) when \( x = 2 \) and \( \frac{dx}{dt} = -1 \).
2. Given \( y = x^4 \), find \( \frac{dy}{dt} \) when \( x = 3 \) and \( \frac{dx}{dt} = 1 \).
3. Given \( y = 2x^2 + x \), find \( \frac{dy}{dt} \) when \( x = -3 \) and \( \frac{dx}{dt} = 2 \).
4. Given \( y = -3x^2 + 2x \), find \( \frac{dy}{dt} \) when \( x = -2 \) and \( \frac{dx}{dt} = 6 \).
5. Given \( y = 2x^3 \), find \( \frac{dx}{dt} \) when \( x = 1 \) and \( \frac{dy}{dt} = 10 \).
6. Given \( y = 4x^2 \), find \( \frac{dx}{dt} \) when \( x = 5 \) and \( \frac{dy}{dt} = -3 \).
7. Given \( y = x - x^4 \), find \( \frac{dx}{dt} \) when \( x = 2 \) and \( \frac{dy}{dt} = -5 \).
8. Given \( y = 5x - x^2 \), find \( \frac{dx}{dt} \) when \( x = -2 \) and \( \frac{dy}{dt} = 2.5 \).
9. Given \( y = e^{2x+1} \), find \( \frac{dy}{dt} \) when \( x = 4 \) and \( \frac{dx}{dt} = 0.5 \).
10. Given \( y = e^{1-3x} \), find \( \frac{dy}{dt} \) when \( x = 2 \) and \( \frac{dx}{dt} = 4 \).
*Note: There are no graphs or diagrams in this exercise set.*
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