$\"\"$

The function is $\"f$ .

$\"fraction$ (Apply derivative with respect to x)

$\"f$ (The sum rule)

$\"f$ ( $\"fraction$ )

$\"f$ (Apply the chain rule)

$\"f$ (Take out common term)

$\"\"$

To find the critical point then f\\'(x) = 0

$\"f$ (Take f\\'(x) = 0)

$\"1$ (Multiply each side by 2)

$\"1$ (Add $\"italic$ to each side)

$\"italic$ (Trigonometric table in sin(90) = 1)

$\"x$ (Multiply each side by 2)

$\"x$ (The critical number)

$\"\"$

Because there are no points for which f\\' does not exist. you can conclude that $\"x$ and $\"fraction$ are the only critical numbers. The table summarizes the testing of the three intervals determined by two critical numbers.

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

\ Interval \	\ $\"minus$ \	\ $\"pi$ \	\ $\"fraction$ \
\ Test Value \	\ $\"x$ \	\ $\"x$ \	\ $\"x$ \
\ Sign of f\\'(x) \	\ $\"f$ \	\ $\"f$ \	\ $\"f$ \
\ Conclusion \	\ Increasing \	\ Increasing \	\ Increasing \

So, f is increasing on the interval $\"open$ . $\"\"$

Therefore f is increasing on the interval $\"open$ .