How would I know the shape of f(x) = 2x + cos (x) without graphing it or computing at ton of values? Sorry if this seems not calculus, but I need it to find an exact root.

Question

anonymous · Answer

would the shape help you determine the exact root..?  its slope is 2 - sin x, which means it's always positive (since |sin x| <= 1).  but because its slope has a sin x in it, it's periodic.

think of it as a wavy line angled up like this

|dw:1382215412464:dw|

it's a bad drawing, but visualize that wavy line as sinusoidal with an upward slope

anonymous · Answer

Its me understand  that since, it is always increasing than there really can only be one root.

anonymous · Answer

oh, right.  because the slope of 2x + cos x is . . 2 - sin x, and 2 - sin x is never negative (always positive), then the slope of the original function is never negative.  if it's never negative, it's always increasing.  if it's always increasing, once it passes the root, it never goes back