With today's technology and powerful computers, it is often tempting to think that the curve sketching process is not needed anymore. However, basing conclusions on a sketch from a computer screen can be risky. That is the case, for instance, with the function f(x)=x* –408x³ +3600x² . Graphing f properly on the screen, in a way that shows its extreme and inflection points is quite difficult. (a) Calculate f' and find the x-values of its local extreme points. (b) Calculate f" and find the x-values of its points of inflection (round your answer to two decimals). (c) Draw a sketch of the graph of f , that clearly shows extreme and inflection points. Make sure to do everything as instructed above. Show and explain ALL your work

With today's technology and powerful computers, it is often tempting to think that the curve sketching process is not needed anymore. However, basing conclusions on a sketch from a computer screen can be risky. That is the case, for instance, with the function f(x)=x* –408x³ +3600x² . Graphing f properly on the screen, in a way that shows its extreme and inflection points is quite difficult. (a) Calculate f' and find the x-values of its local extreme points. (b) Calculate f" and find the x-values of its points of inflection (round your answer to two decimals). (c) Draw a sketch of the graph of f , that clearly shows extreme and inflection points. Make sure to do everything as instructed above. Show and explain ALL your work

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter5: Exponential And Logarithmic Functions

Section5.2: Applications Of Exponential Functions

Problem 47E

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