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

question 142

Multiple Choice

Find the points of inflection and discuss the concavity of the function $f ( x ) = - \sin x + \cos x \text { on the interval } ( 0,2 \pi )$ .

• A) no inflection points. concave up on \(( 0,2 \pi )\)
• B) concave upward on \(\left( 0 , \frac { 1 } { 2 } \pi \right)\); concave downward on \(\left( \frac { 5 } { 2 } \pi , 2 \pi \right)\); inflection point at \(\left( 0 , \frac { 1 } { 2 } \pi \right)\)
• C) no inflection points. concave down on \(( 0,2 \pi )\)
• D) concave downward on \(\left( 0 , \frac { 1 } { 2 } \pi \right)\); concave upward on \(\left( \frac { 5 } { 2 } \pi , 2 \pi \right)\); inflection point at \(\left( 0 , \frac { 1 } { 2 } \pi \right)\)
• E) none of the above

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