Find the points of inflection of the graph of the function. (Order your answers from smallest to largest x, then from smallest to largest y. If an answer does not exist, enter DNE.) f(x) = 6x – x2 (х, у) — (x, y) = %3D Describe the concavity. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) concave upward concave downward

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
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### Finding Points of Inflection and Describing Concavity

**Task:**
Find the points of inflection of the graph of the function. (Order your answers from smallest to largest \( x \), then from smallest to largest \( y \). If an answer does not exist, enter DNE.)

\[ f(x) = 6x^4 - x^2 \]

Points of Inflection:
\[ (x, y) = \left( \boxed{\phantom{0}} \right) \]
\[ (x, y) = \left( \boxed{\phantom{0}} \right) \]

Describe the concavity. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)

Concave Upward:
\[ \boxed{\phantom{0}} \]

Concave Downward:
\[ \boxed{\phantom{0}} \]
Transcribed Image Text:### Finding Points of Inflection and Describing Concavity **Task:** Find the points of inflection of the graph of the function. (Order your answers from smallest to largest \( x \), then from smallest to largest \( y \). If an answer does not exist, enter DNE.) \[ f(x) = 6x^4 - x^2 \] Points of Inflection: \[ (x, y) = \left( \boxed{\phantom{0}} \right) \] \[ (x, y) = \left( \boxed{\phantom{0}} \right) \] Describe the concavity. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) Concave Upward: \[ \boxed{\phantom{0}} \] Concave Downward: \[ \boxed{\phantom{0}} \]
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