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

---

Definitions:

Philosophical Statement

An expression or articulation of fundamental beliefs or guiding principles related to philosophy.

Continental Congress

A convention of delegates from the Thirteen Colonies that became the governing body of the United States during the American Revolution.

Articles of Confederation

The original constitution of the United States, ratified in 1781, which was replaced by the U.S. Constitution in 1789 due to its inadequacies in governing the new nation.

Unanimous Vote

A unanimous vote occurs when all members of a decision-making body agree on a particular decision or motion without any dissent.