Use the Linear Approximation to estimate Δ𝑓=(10.4)^1/4−(10)^1/4.

Answer 1

f(x) = x^(1/4)
f'(x) = 1 / 4x^(3/4)
f'(10) = 1 / 4∜1000 ≈ 0.0444
so at x=10, Δf/Δx ≈ df/dx.
Δf ≈ f'(10)*Δx = 0.444 * 0.4 = 1.9559