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 (6,0). unfortunately, the existing gas line follows the curve y=√16x2 6x 19. it costs 300 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

The cost for the hook is calculated by
C = (y - 0)(300)
C = √(16x2 + 6x + 19)
To get the minimum, take the derivative of C in terms of x and equate it to zero. Solve for x and substitute it back to C to solve for the minimum cost.