The graph of the function [tex]f(x)[/tex] is
Find [tex]f''(x):[/tex]
1.
[tex]f'(x)=(x-4\cos x)'=1+4\sin x;[/tex]
2.
[tex]f''(x)=4\cos x.[/tex]
Now:
1. when [tex]4\cos x>0,[/tex] the graph of the function is concave upward and this is for
[tex]x\in \left(-\dfrac{\pi}{2}+2\pi k,\dfrac{\pi}{2}+2\pi k\right), \text{ where } k\in Z.[/tex]
2. when [tex]4\cos x<0,[/tex] the graph of the function is concave downward and this is for
[tex]x\in \left(\dfrac{\pi}{2}+2\pi k,\dfrac{3\pi}{2}+2\pi k\right), \text{ where } k\in Z.[/tex]
