Question

Find any intervals where the function f(x)=−(5x+5sin(x)),0≤x≤2π is increasing/decreasing.

Answer 1

is x in radians or degrees?

Answer 2

If x is in radians, then f(x) is decreasing from [0, π) and at (π, 2π], or 0≤x<π and π<x≤2π.

Answer 3

I think radians. If it's not then I can just do any conversions to degrees.

Answer 4

You guys are awesome. Thanks!

Answer 5

In degrees, it is just a constantly decreasing linear function, so x is in radians.

Answer 6

You're welcome

Answer 7

f(x)=−(5x+5sin(x)) = -5(x + sinx)
f'(x) = -5(1+cosx)
clearly f' < 0 for all x where cosx > -1. That is all real values except odd multiples of π.