Homework Help is Here – Start Your Trial Now!
Math
Calculus
Compute -(-x - 3x²-x). ď² da²

Compute -(-x - 3x²-x). ď² da²

Calculus: Early Transcendentals
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...
See similar textbooks
icon
Related questions
Question
**Problem Statement:** Compute \(\frac{d^2}{dx^2} \left( -x^4 - 3x^2 - x \right)\). **Context:** The task is to find the second derivative of the polynomial function \(-x^4 - 3x^2 - x\) with respect to \(x\). This involves differentiating the given function twice to determine how the rate of change itself changes with \(x\). **No Graphs or Diagrams Present.** Explanation of Solution: 1. **First Derivative** (\(f'(x)\)): - Start by differentiating each term of the function with respect to \(x\). - \(-x^4 \) differentiates to \(-4x^3\). - \(-3x^2 \) differentiates to \(-6x\). - \(-x\) differentiates to \(-1\). 2. **Second Derivative** (\(f''(x)\)): - Differentiate each term of the first derivative. - \(-4x^3\) differentiates to \(-12x^2\). - \(-6x\) differentiates to \(-6\). - The derivative of \(-1\) is \(0\). Thus, the second derivative of the function is \(f''(x) = -12x^2 - 6\).
Transcribed Image Text:**Problem Statement:** Compute \(\frac{d^2}{dx^2} \left( -x^4 - 3x^2 - x \right)\). **Context:** The task is to find the second derivative of the polynomial function \(-x^4 - 3x^2 - x\) with respect to \(x\). This involves differentiating the given function twice to determine how the rate of change itself changes with \(x\). **No Graphs or Diagrams Present.** Explanation of Solution: 1. **First Derivative** (\(f'(x)\)): - Start by differentiating each term of the function with respect to \(x\). - \(-x^4 \) differentiates to \(-4x^3\). - \(-3x^2 \) differentiates to \(-6x\). - \(-x\) differentiates to \(-1\). 2. **Second Derivative** (\(f''(x)\)): - Differentiate each term of the first derivative. - \(-4x^3\) differentiates to \(-12x^2\). - \(-6x\) differentiates to \(-6\). - The derivative of \(-1\) is \(0\). Thus, the second derivative of the function is \(f''(x) = -12x^2 - 6\).
Expert Solution
Step 1

Calculus homework question answer, step 1, image 1

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS