Compute Δy and dy for the given values of x and dx = Δx.

Question

Compute Δy and dy for the given values of x and dx = Δx.

y = x² − 6x, x = 5, Δx = 0.5

Answer 1

Let y = f(x) = x² - 6x

Then, Δy = f(x + Δx) - f(x) = f(5.5) - f(5) = -2.75 - (-5) = 2.25

dy = f'(x)dx = f'(5)(0.5) = 4(0.5) = 2