- #1

Cosmophile

- 111

- 2

## Homework Statement

Consider only values of ##x \geq 0##, and let ##f(x) = -x + \frac {x^3}{3!} + \sin x##. Show whether ##f## is increasing or decreasing.

## Homework Equations

[tex] f(x) = -x + \frac {x^3}{3!} + \sin x [/tex]

[tex] f'(x) = -1 + \frac {x^2}{2} + \cos x [/tex]

## The Attempt at a Solution

I know that ##f## is increasing whe ##f' > 0##, and that ##f## is decreasing when ##f' < 0##. In the first case, I have [tex] f'(x) = -1 + \frac {x^2}{2} + \cos x > 0 [/tex]

[tex] x^2 + 2 \cos x > 2 [/tex]

[tex] |x| > 2|(1- \cos x)| [/tex]

Unfortunately, I'm having a hard time making any sense of this solution. For some reason, trigonometric functions are the only functions I've dealt with that give me any issue with these types of problems. It's demoralizing, really. Anyway, any help is greatly appreciated, as always!