Answer :

Let us assume that


Also, let x = 27 so that x + Δx = 25


27 + Δx = 25


Δx = –2


On differentiating f(x) with respect to x, we get



We know





When x = 27, we have







Recall that if y = f(x) and Δx is a small increment in x, then the corresponding increment in y, Δy = f(x + Δx) – f(x), is approximately given as



Here, and Δx = 2


Δf = (0.03704)(–2)


Δf = –0.07408


Now, we have f(25) = f(27) + Δf




f(25) = 3 0.07408


f(25) = 2.92592


Thus, (25)1/3 ≈ 2.92592


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