Compute Δy and dy for the given values of x and dx = Δx. (Round your answers to three decimal places.) y = 3x - x², x = 3, Δx = -0.6, Δy=?

Solution:

Given y = 3x - x², x = 3, Δx = -0.6

We have Δy = small change in y

Δx = small change in x

Δy = dy / dx . Δx -----(1)

y = 3x - x² ----(2)

Differentiating equation (2) w.r.t. X,

dy/dx = 3 - 2x

∴ (dy/dx)x = 3 = 3 - 2(3) = -3

Substituting in equation (1)

Δy = (-3) (-0.6)

Δy = 1.8

Compute Δy and dy for the given values of x and dx = Δx. (Round your answers to three decimal places.) y = 3x - x², x = 3, Δx = -0.6, Δy=?

Summary:

The value of Δy, where y = 3x - x², x = 3, Δx = -0.6, is 1.8.