CALCULUS PROBLEM PLEASE HELP?

Question

The exercise tells me to compare delta y and dy. 

1) y=1-2x^2 x=0 dx= -.01

Answer 1

1)

y = 1-2x²

x=0 , dx= - 0.01

Computing of dy :

y = 1-2x²

Apply derivative with respect to x

dy/dx = 1-2*2x

dy = (1 - 4x)dx

Substitute x = 0 , dx = - 0.01

dy = (1 - 4*0)(- 0.01)

dy = - 0.01

Computing of Δy :

y = 1-2x²

y(0) = 1-2*0² = 1

y(-0.01) = 1-2(-0.01)² = 0.9998

Δy = y(0) - y(-0.01) = 1 - 0.9998

Δy = 0.0002

Solution : dy = - 0.01 , Δy = 0.0002