(Solved): 2. a. Fill in the blank: If a function g has a local maximum or minimum at , and if g() exis ...

2. a. Fill in the blank: If a function $g$ has a local maximum or minimum at $\theta$, and if $g^{\prime }(\theta )$ exists, then b. Let $g(\theta )={\cos }^2\theta -2\sin \theta ,0\le \theta \le 2\pi$. i. Find the critical points of $g(\theta )$. (Use algebra and calculus to find them. Do NOT sketch the graph of $g(\theta )$.) ii. Find the absolute maximum and the absolute minimum of $g(\theta )$ over the interval $[0,2\pi ]$. (Do not sketch the graph of $g(\theta )$.) 3. Two cars start moving from the same point. One travels north at 25 miles per hour and the other travels east at 60 miles per hour. At what rate is the distance between the cars increasing, two hours later?