With today's technology and powerful computers, it is often tempting to think that the curve sketching process is not needed anymore. However, basing our conclusions on a sketch from a computer screen can be risky. That is the case, for instance, with the function f(x)=x4-408x³ +3600x². Graphing f(x) properly on the screen, in a way that shows its extreme and inflection points is quite difficult. (a) Calculate f '(x) and find the x-values of its local extreme points. (b) Calculate f "(x) 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(x), that clearly shows extreme and inflection points.
With today's technology and powerful computers, it is often tempting to think that the curve sketching process is not needed anymore. However, basing our conclusions on a sketch from a computer screen can be risky. That is the case, for instance, with the function f(x)=x4-408x³ +3600x². Graphing f(x) properly on the screen, in a way that shows its extreme and inflection points is quite difficult. (a) Calculate f '(x) and find the x-values of its local extreme points. (b) Calculate f "(x) 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(x), that clearly shows extreme and inflection points.
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...
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Transcribed Image Text:With today's technology and powerful computers, it is often tempting to think that the curve sketching
process is not needed anymore. However, basing our conclusions on a sketch from a computer screen can
be risky.
That is the case, for instance, with the function f(x)=x4-408x³+3600x².
Graphing f(x) properly on the screen, in a way that shows its extreme and inflection points is quite
difficult.
(a) Calculate f '(x) and find the x-values of its local extreme points.
(b) Calculate f "(x) 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(x), that clearly shows extreme and inflection points.
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