Use a linear approximation to estimate the number (64.07)2/3.

Question

Use a linear approximation to estimate the number (64.07)^2/3

Make sure that your answer is correct to at least 9 decimal places.

answer: ___

Answer 1

Let y = x^2/3 The point (64, 64^2/3) = (64, 16) is on the graph.

y' = (2/3)x^-1/3 Slope of tangent at (64, 16) is (2/3)(64^-1/3) = 1/6

Tangent line equation: y - 16 = (1/6)(x - 64)

So, y = 16 + (1/6)(x - 64)

(64.07)^2/3 ≈ 16 + (1/6)(64.07 - 64) = 16.011666667