Calculus Question w/ Linear Approx

Question

let y = 2(sqrt(x))

Find the change in y when x= 4 and change of x = 0.3 ______________

Find the differential dy when x = 4 and dx = 0.3 _________________

Answer 1

f(4) = 2√4 = 4; Δx = 0.3; x + Δx = 4.3; Δf = f (4.3) - f(4) = 2√4.3 - 2√4 = 0.1473

f'(x) = 1/√x; f'(4) = 1/2; df = f'(4)dx = 1/2·0.3 = 0.15;

So, Δf ≈ df