Determine the Open Intervals on Which the Graph of the Function

question 75

Multiple Choice

Determine the open intervals on which the graph of the function $y = 3 x - \tan x , \left( - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right) \text { is concave upward or concave downward. }$

• A) concave upward: \(\left( 0 , \frac { \pi } { 2 } \right) ;\) concave downward: \(\left( - \frac { \pi } { 2 } , 0 \right)\)
• B) concave upward: \(\left( - \frac { \pi } { 2 } , - \frac { \pi } { 6 } \right) , \left( \frac { \pi } { 6 } , \frac { \pi } { 2 } \right) ;\) concave downward: \(\left( - \frac { \pi } { 6 } , \frac { \pi } { 6 } \right)\)
• C) concave upward: \(\left( - \frac { \pi } { 2 } , 1 \right) ;\) concave downward: \(\left( 1 , \frac { \pi } { 2 } \right)\)
• D) concave upward: \(\left( - \frac { \pi } { 6 } , \frac { \pi } { 6 } \right) ;\) concave downward: \(\left( - \frac { \pi } { 2 } , - \frac { \pi } { 6 } \right) , \left( \frac { \pi } { 6 } , \frac { \pi } { 2 } \right)\)
• E) concave upward: \(\left( - \frac { \pi } { 2 } , 0 \right) ;\) concave downward: \(\left( 0 , \frac { \pi } { 2 } \right)\)

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