A particle moves along the curve y=2x^3-4x+1.

a particle moves along the curve y=2x^3-4x+1. what is the rate of change of its y-coordinate, in cm/sec, when the particle crosses the y-axis if the rate of change of its x-coordinate is constant at 3 cm/sec?

a. 2 cm/sec
b. -2 cm/sec
c. -6 cm/sec
d. -10 cm/sec
e. -12 cm/sec

Calculus

y=2x^3-4x+1
dy/dt = (6x^2-4) (dx/dt)
dy/dt = 3 cm/sec (given)
When the particle crosses the y-axis, x=0

dy/dt = [ 6 (0)^2 -4 ] (3) = -12 cm/sec

y = 2x^2 - 4x + 1
y = 1 when x = 0

dy/dt = (4x - 4) dx/dt
dydt = (-4)(3 cm/sec) = -12 cm/sec

e

rate of change of its y-coordinate
-4 + 6 x^2

e