need help with this calculus problem

Question

Find a linearization of the function f(x) = ³√( 1−x) at a = 0.

cuberoot√ (1−x) =?

Answer 1

f(x) = (1 - x)^1/3; x = 0, y = f(0) = 1. So we have point (0,1).

f'x) = - 1/3(1 - x)^{- 2/3}; f'(0) = - 1/3.

So, linearization for f(x) = (1 - x)^1/3 = 1 -1/3(x - 0) = 1 - x/3

Answer 2

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