$\displaystyle f(x)=0.002x^3-0.08x^2+x$
Interval: 0 < x < 50
I need to find the x-intervals, where the slope-angles are between 0 and 45 degrees with the x-axis' positive direction.
I'm kinda lost?
1. Draw a graph of y = f(x)
2. Find f'(x).
3. Draw a graph of y = f'(x).
4. Note that m = f'(x) = tan (theta) where theta is the angle between the x-axis's positive direction.
5. Solve tan(0) < f'(x) < tan(45) <=> 0 < f'(x) < 1 (all angle sin degrees). The graph of y = f'(x) might help to see what's happening with this inequation.