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Determine the open interval on which the graph is concave upward or concave downward. (Enter the ...

Question:

Determine the open interval on which the graph is concave upward or concave downward. (Enter the answer using interval notation. If an answer does not exist, enter DNE.

{eq}y = 3x^2 - x -6 {/eq}

Concave upward {eq}\rule{20mm}{.5pt} {/eq}

Concave downward {eq}\rule{20mm}{.5pt} {/eq}

Concavity of Function:

Given a function {eq}f(x) {/eq}

inflection points arise when second order derivative {eq}f''(x)=0 {/eq}.

Morever, the function is concave up when {eq}f''(x) >0 {/eq} and concave down when {eq}f''(x) <0 {/eq}

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Concavity and Inflection Points on Graphs

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Chapter 9 / Lesson 5
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