Calculus Question

Question

Suppose y =

2x + 1

,

 where x and y are functions of t.

(a) If dx/dt = 6, find dy/dt when x = 4.

dy/dt=_____

(b) If dy/dt = 3, find dx/dt when x = 24.

dx/dt=_____

Answer 1

y = √(2x+1)

dy/dx = 1/√(2x+1)

a) dy/dt = (dy/dx) • (dx/dt)

dy/dt = [1/√(2(4)+1)] • [6] = (1/3)(6) = 2

b) dx/dt = (dy/dt) / (dy/dx)

dx/dt = [3] / [1/√(2(24)+1)] = (3) / (1/7) = 21