1. Find all of the critical points and locam max and min of the function f(x)=x³- 6x² + 5

2. Find the shortest distance from a point (3,5) to the graph y=x²

^3. Consider yourself as an entrepreneur at the Mall selling 5000 donuts a day at 50 each. When you raised the price to 70 each, the sale dropped to 4000 donuts per day. Now, assume that there is a linear relationship between the price and number of donuts sold. Further assume that there is a fix cost (overhead) of $1000 per day and the cost of each donut is 25. What would be the price of the donut to maximize the profit?

4. Given the function: .

a). Find all critical points

b). Characterize each of the critical points