Determine the Open Intervals on Which the Graph of the Function

question 69

Multiple Choice

Determine the open intervals on which the graph of the function
$f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 625 }$ is concave upward or concave downward.

• A) concave upward: \(\left( - \infty , - \frac { 25 \sqrt { 3 } } { 3 } \right) , \left( \frac { 25 \sqrt { 3 } } { 3 } , \infty \right) ;\) concave downward: \(\left( - \frac { 25 \sqrt { 3 } } { 3 } , \frac { 25 \sqrt { 3 } } { 3 } \right)\)
• B) concave upward: \(\left( - \frac { 25 \sqrt { 3 } } { 3 } , \frac { 25 \sqrt { 3 } } { 3 } \right) ;\) concave downward: \(\left( - \infty , - \frac { 25 \sqrt { 3 } } { 3 } \right) , \left( \frac { 25 \sqrt { 3 } } { 3 } , \infty \right)\)
• C) concave upward: \(( - \infty , 0 )\); concave downward: \(( 0 , \infty )\)
• D) concave upward: \(\left( - \frac { 625 } { 3 } , \frac { 625 } { 3 } \right) ;\) concave downward: \(\left( - \infty , - \frac { 625 } { 3 } \right) , \left( \frac { 625 } { 3 } , \infty \right)\)
• E) concave upward: \(\left( - \infty , - \frac { 625 } { 3 } \right) , \left( \frac { 625 } { 3 } , \infty \right) ;\) concave downward: \(\left( - \frac { 625 } { 3 } , \frac { 625 } { 3 } \right)\)

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