Determine the Open Intervals on Which the Graph Of $f ( x ) = 5 x + 7 \cos x$

question 126

Multiple Choice

Determine the open intervals on which the graph of $f ( x ) = 5 x + 7 \cos x$ is concave downward or concave upward.

• A) concave downward on \(\ldots , \left( - \frac { 3 \pi } { 2 } , - \frac { \pi } { 2 } \right) , \left( \frac { \pi } { 2 } , \frac { 3 \pi } { 2 } \right) , \left( \frac { 5 \pi } { 2 } , \frac { 7 \pi } { 2 } \right) , \ldots ;\) concave upward on \(\ldots , \left( - \frac { 5 \pi } { 2 } , - \frac { 3 \pi } { 2 } \right) , \left( - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right) , \left( \frac { 3 \pi } { 2 } , \frac { 5 \pi } { 2 } \right) , \ldots\)
• B) concave downward on \(\ldots , \left( - \frac { 3 \pi } { 4 } , - \frac { \pi } { 4 } \right) , \left( \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } \right) , \left( \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 } \right) , \ldots ;\) concave upward on \(\ldots , \left( - \frac { 5 \pi } { 4 } , - \frac { 3 \pi } { 4 } \right) , \left( - \frac { \pi } { 4 } , \frac { \pi } { 4 } \right) , \left( \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } \right) , \ldots\)
• C) concave upward on \(\ldots , \left( - \frac { 3 \pi } { 4 } , - \frac { \pi } { 4 } \right) , \left( \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } \right) , \left( \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 } \right) , \ldots ;\) concave downward on \(\ldots , \left( - \frac { 5 \pi } { 4 } , - \frac { 3 \pi } { 4 } \right) , \left( - \frac { \pi } { 4 } , \frac { \pi } { 4 } \right) , \left( \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } \right) , \ldots\)
• D) concave downward on \(\ldots , \left( - \frac { 3 \pi } { 6 } , - \frac { \pi } { 6 } \right) , \left( \frac { \pi } { 6 } , \frac { 3 \pi } { 6 } \right) , \left( \frac { 5 \pi } { 6 } , \frac { 7 \pi } { 6 } \right) , \ldots ;\) concave upward on \(\cdots \left( - \frac { 5 \pi } { 6 } , - \frac { 3 \pi } { 6 } \right) , \left( - \frac { \pi } { 6 } , \frac { \pi } { 6 } \right) , \left( \frac { 3 \pi } { 6 } , \frac { 5 \pi } { 6 } \right) , \ldots\)
• E) concave upward on \(\ldots , \left( - \frac { 3 \pi } { 2 } , - \frac { \pi } { 2 } \right) , \left( \frac { \pi } { 2 } , \frac { 3 \pi } { 2 } \right) , \left( \frac { 5 \pi } { 2 } , \frac { 7 \pi } { 2 } \right) , \ldots\); concave downward on \(\ldots , \left( - \frac { 5 \pi } { 2 } , - \frac { 3 \pi } { 2 } \right) , \left( - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right) , \left( \frac { 3 \pi } { 2 } , \frac { 5 \pi } { 2 } \right) , \ldots\)

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