How do you use a linear approximation to approximate the value of #root(3)(27.5)#?
1 Answer
Aug 23, 2017
We let
We compute the derivative of
#f(a) = a^(1/3) -> f'(a) = 1/3a^(-2/3)#
Hence,
#f'(27) = 1/3(27)^(-2/3) =1/3(3)^(-2) = 1/3(1/9) = 1/27#
Recalll the equation of a line is given by
#y - y_1 = m(x - a)#
#y - 3 = 1/27(x - 27)#
#y = 1/27x - 1+ 3#
#y = 1/27x + 2#
So the approximation at
#y ~~ 1/27(27.5) + 2 ~~ 3.0185185...#
If we use a calculator to compute we get
Hopefully this helps!