(Solved): Consider the following. (If an answer does not exist, enter DNE.) f(x)=5sin(x)+5cos(x),0x2 ...

Consider the following. (If an answer does not exist, enter DNE.) $f(x)=5\sin (x)+5\cos (x),0\le x\le 2\pi$ (a) Find the interval(s) on which $f$ is increasing. (Enter your answer using interval notation.) $\left(0,\frac{\pi }{4}\right)\cup \left(\frac{5\pi }{4},2\pi \right)$ (b) Find the interval(s) on which $f$ is decreasing. (Enter your answer using interval notation.) $\left(\frac{\pi }{4},\frac{5\pi }{4}\right)$ (c) Find the local minimum and maximum values of $f$. local minimum value local maximum value