Calculus Question

Question

A particle is moving along the curve y=3(√4x+1). As the particle passes through the point (2,9), its x-coordinate increases at a rate of 5 units per second. Find the rate of change of the distance from the particle to the origin at this instant.

Answer 1

Distance f(x) = (x² + 36x + 9)^1/2; f'(x) = 1/2(x² + 36x + 1)^-1/2 ·(2x + 36)dx/dt = 1/2(4 + 72 + 9)^-1/2(40)·5units/s =

10.54 units/s