Homework Help is Here – Start Your Trial Now!
Math
Calculus
2. Use Desmos to graph the function y³ + y² + x² - 3y² = 0 and estimate the slope of the tangent line at (-1,1). Then find using implicit differentiation and plug in = -1 and y = 1. Compare and discuss the estimated slope with the slope you found analytically.

2. Use Desmos to graph the function y³ + y² + x² - 3y² = 0 and estimate the slope of the tangent line at (-1,1). Then find using implicit differentiation and plug in = -1 and y = 1. Compare and discuss the estimated slope with the slope you found analytically.

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Polynomial And Rational Functions
Section9.4: Graphing Polynomial Functions
Problem 44PS: A company determines that its weekly profit from manufacturing and selling x units of a certain item...
See similar textbooks
icon
Related questions
Question
Q2&Q3 needed to be solved correctly in 30 minutes and get the thumbs up please show neat and clean work for it By hand solution needed Please solve both question Compeltely
1. Chains Inc. is in the business of making and selling chains. Let c(t)be the number of miles of chain produced after thours of production. Let p(c) be the profit as a function of the number of miles of chain produced and let g(t) be the profit as a function of the number of hours of production. Suppose the company can produce 3 miles of chain per hour and suppose their profit on the chains is $4000 per mile of chain. Find and interpret (use complete sentences) each of the following (include units), c' (t) p'(c), and d' (t). How does d (t) relates to p'(c)and c(t)? 2. Use Desmos to graph the function y³ +yx²+x² − 3y² = 0) and estimate the slope of the tangent line at (-1,1). Then find using implicit differentiation and plug in x = -1 and y = 1. Compare and discuss the estimated slope with the slope you found analytically. 3. Let f(x) = (3x² + 1)2. Find f'(x) in 3 different ways by following the instructions below in parts a, b and c: a) Develop the identity f(x) then take the derivative. b) View f(x) as (3x² + 1) (3x² + 1) and use the product rule to find f'(x). c) Apply the chain rule directly to the expression f(x) = (3x² + 1)². d) Are your answers in parts a, b, c the same? Why or why not?
Transcribed Image Text:1. Chains Inc. is in the business of making and selling chains. Let c(t)be the number of miles of chain produced after thours of production. Let p(c) be the profit as a function of the number of miles of chain produced and let g(t) be the profit as a function of the number of hours of production. Suppose the company can produce 3 miles of chain per hour and suppose their profit on the chains is $4000 per mile of chain. Find and interpret (use complete sentences) each of the following (include units), c' (t) p'(c), and d' (t). How does d (t) relates to p'(c)and c(t)? 2. Use Desmos to graph the function y³ +yx²+x² − 3y² = 0) and estimate the slope of the tangent line at (-1,1). Then find using implicit differentiation and plug in x = -1 and y = 1. Compare and discuss the estimated slope with the slope you found analytically. 3. Let f(x) = (3x² + 1)2. Find f'(x) in 3 different ways by following the instructions below in parts a, b and c: a) Develop the identity f(x) then take the derivative. b) View f(x) as (3x² + 1) (3x² + 1) and use the product rule to find f'(x). c) Apply the chain rule directly to the expression f(x) = (3x² + 1)². d) Are your answers in parts a, b, c the same? Why or why not?
Expert Solution
steps

Step by step

Solved in 4 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra for College Students
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS