Find the Interval on Which $f ( x ) = x + \cos x , 0 \leq x \leq 2 \pi$

question 181

Multiple Choice

Find the interval on which $f ( x ) = x + \cos x , 0 \leq x \leq 2 \pi$ is increasing.

• A) \(\left[ \frac { \pi } { 3 } , \frac { 5 \pi } { 3 } \right]\)
• B) \(\left[ 0 , \frac { \pi } { 3 } \right]\)
• C) \(\left[ \frac { 5 \pi } { 3 } , 2 \pi \right]\)
• D) \(\left[ 0 , \frac { \pi } { 2 } \right]\)
• E) \(\left[ \frac { \pi } { 2 } , \frac { 3 \pi } { 2 } \right]\)
• F) \(\left[ \frac { 3 \pi } { 2 } , 2 \pi \right]\)
• G) \([ 0 , \pi ]\)
• H) \([ \pi , 2 \pi ]\)

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Definitions:

Biological Catalysts

Enzymes that speed up chemical reactions in biological processes without being consumed.

Enzymes

Biological catalysts that speed up chemical reactions in living organisms by lowering the activation energy.

Phosphorylation Reaction

A chemical process that involves the addition of a phosphate group to a molecule, often altering the function of proteins.

Glucose-P

Refers to phosphorylated forms of glucose, which play critical roles in cellular energy metabolism and regulatory pathways.