Help me with calculus

Question

Use the differential dy to approximate Δy when x changes from x=2 to x=2.07

y=√(3x-2)

Answer 1

f(x) = √3x - 2); f(2) = 2; we have to evaluate f(2.07)

f(2.07) = f(2) + Δf(2); Δf(2) ≈ df(2); f'(x) = 3/(2√3x - 2); f'(2) = 3/4; dx = Δx = 2.07 - 2 = 0.07

f(2.07) ≈ 2 + 3/4(0.07) = 2.0525