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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Definitions:

Intrinsic Case Study

A case study where the interest is in the case itself because of its unique or peculiar nature, rather than to generalize or compare.

Local Middle School

An educational institution typically serving students in the intermediate grades, often grades 6 through 8, within a local community.