(Solved): Consider the following function on the given interval. f(t)=2cos(t)+sin(2t),[0,2] Find the der ...

Consider the following function on the given interval. $f(t)=2\cos (t)+\sin (2t),\left[0,\frac{\pi }{2}\right]$ Find the derivative of the function. $f^{\prime }(t)=$ Find any critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) $t=$ Find the absolute maximum and absolute minimum values of $f$ on the given interval. absolute minimum value absolute maximum value