An ant is moving along the curve y = √x. As the ant passes through the point (4, 2), its x-coordinate increases at a rate of 5 cm/s. How fast is the distance to the origin changing at this instant?

Answer 1

Distance to origin s = √x² + x; ds/dt = 1/(2√x² + x)(2xdx/dt + dx/dt) = 1/(2√16 + 4)(2·4·5 + 5) = 45/(2√20) =

45/(4√5) = 9√5/4 = 5.03 cm/s