Question

You are building a new house on a cartesian plane whose units are measured in miles. Your house is to be located at the point (2,0) . Unfortunately, the existing gas line follows the curve y= √(16 x^2 +5x+16). It costs 400 dollars per mile to install new pipe connecting your house to the existing line. What is the least amount of money you could pay to get hooked up to the system?

Answer 1

find the derivative of the equation to find its critical points. And the compute the distance from the house to the critical point (local minimum).However, I'm unable to compute the derivative. Kindly help with explanation.