Compute Δy and dy for the given values of x and dx = Δx. (Round your answers to three decimal places.). y = 2x - x^2, x = 2, Δx = - 0.6. Find: Δy and dy

Y = 2x - x^2

Differentiating gives: dy/dx = 2 - 2x

dy = (2-2x) dx

If x changes by a small amount (Δx), this will cause y to change by a small amount (Δy). Providing Δx and Δy are small, to a good approximation we can write:

Δy = (2-2x) Δx

So if x = 2 and Δx = - 0.4:

Δy = (2-2x2) (-0.4)

= - 2 x (-0.4)

= 0.8