Question

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

Answer 1

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