Find the Points of Inflection and Discuss the Concavity of the Function

question 16

Multiple Choice

Find the points of inflection and discuss the concavity of the function. $f ( x ) = 7 x ^ { 3 } + 8 x ^ { 2 } + 5 x - 8$

• A)inflection point at \(x = - \frac { 8 } { 21 }\) ; concave downward on \(\left( - \infty , - \frac { 8 } { 21 } \right)\) ; concave upward on \(\left( - \frac { 8 } { 21 } , \infty \right)\)
• B)inflection point at \(x = - \frac { 8 } { 21 }\) ; concave upward on \(\left( - \infty , - \frac { 8 } { 21 } \right)\) ; concave downward on \(\left( - \frac { 8 } { 21 } , \infty \right)\)
• C)inflection point at \(x = \frac { 8 } { 21 }\) ; concave downward on \(\left( - \infty , \frac { 8 } { 21 } \right)\) ; concave upward on \(\left( \frac { 8 } { 21 } , \infty \right)\)
• D)inflection point at \(x = \frac { 8 } { 21 }\) ; concave upward on \(\left( - \infty , \frac { 8 } { 21 } \right)\) ; concave downward on \(\left( \frac { 8 } { 21 } , \infty \right)\)
• E)none of the above

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