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
Use derivative rules to find the general derivative:
![The function \( h(x) \) is defined as:
\[
h(x) = \frac{x^3}{2} - \frac{4x^2}{3} + 2x
\]
This expression represents a polynomial function of degree three. Each term in the equation is as follows:
1. \( \frac{x^3}{2} \): The cubic term divided by 2.
2. \( -\frac{4x^2}{3} \): The quadratic term multiplied by 4 and divided by 3.
3. \( +2x \): A linear term with a coefficient of 2.
This polynomial can be used for various calculations, including finding roots, critical points, and analyzing the behavior of the function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4fdd89bf-1afd-4de8-98d6-2edfee28e4a1%2Fda0dd11c-9375-498b-b4d0-9ddf4d12c6ac%2Frs9zkkb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The function \( h(x) \) is defined as:
\[
h(x) = \frac{x^3}{2} - \frac{4x^2}{3} + 2x
\]
This expression represents a polynomial function of degree three. Each term in the equation is as follows:
1. \( \frac{x^3}{2} \): The cubic term divided by 2.
2. \( -\frac{4x^2}{3} \): The quadratic term multiplied by 4 and divided by 3.
3. \( +2x \): A linear term with a coefficient of 2.
This polynomial can be used for various calculations, including finding roots, critical points, and analyzing the behavior of the function.
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