1. Complete the following analysis for the function f(x) = = Note that the first and second derivatives have already been calculated for you! -6x² +6 12x4 - 24 x5 ƒ'(x) = ƒ"(x) = x4 a) Determine the equations of all asymptotes. 6x²-2 x3 b) Calculate the x- and y-intercepts.

Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.2: Introduction To Conics: parabolas
Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.
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1. Complete the following analysis for the function f(x) =
=
Note that the first and second derivatives have already been calculated for you!
12x4 - 24
x5
f'(x) =
=
-6x² +6
x4
f"(x) =
a) Determine the equations of all asymptotes.
b) Calculate the x- and y-intercepts.
6x²-2
x3
Transcribed Image Text:1. Complete the following analysis for the function f(x) = = Note that the first and second derivatives have already been calculated for you! 12x4 - 24 x5 f'(x) = = -6x² +6 x4 f"(x) = a) Determine the equations of all asymptotes. b) Calculate the x- and y-intercepts. 6x²-2 x3
c) Calculate and classify any critical points and any points of inflection. Examine
the concavity of the function.
d) Use your analysis from above to sketch the graph of the function.
-8 -6
-4
22.
8-
6+
4
4
-6
y
6 8
X
1
Transcribed Image Text:c) Calculate and classify any critical points and any points of inflection. Examine the concavity of the function. d) Use your analysis from above to sketch the graph of the function. -8 -6 -4 22. 8- 6+ 4 4 -6 y 6 8 X 1
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