1.Find the maximum and minimum values attained by the function:

f(x)= x+ 5/x

2. Given the function: f(x) = (1+x)^3/2 - 3/2x - 1

Prove that it is increasing on (0, +infinity ) analytically, without relying on a graph.

3. Giving a vertical velocity v(t)= 4t +3 (ft/sec) for a helicopter t seconds after took off. The helicopter was observed 16 feet above the sea level, after taking off for 2 seconds.Find a formula that gives height of the helicopter at any time t? (Hint: v(t)=h'(t) where h(t) is the height of the helicopter at any time t.)

4. Consider yourself as an entrepreneur at the Mall selling 6000 donuts a day at 50 each. When you raised the price to 70 each, the sale dropped to 5000 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?