Production function problem of intermediate microeconomics

Nice function means:

• function is increasing and twice differentiable in all inputs
• isoquant curve is decreasing and convex
• Isoquant curve never touches axes
• Isoquant curve is differentiable
  

Problem 3. Suppose production function is f(k,l) = min{k, l}. a. Is the production function \"nice\"? Explain. b. Find the total cost function C(v, w, q)