## anonymous 4 years ago use a tangent line at (27,3) to the fxn y=x^(1/3) to estimate (25)^(1/3)

First find the slope using $$y'=(1/3)x^{-2/3}$$. At $$x=27$$ we have $$y'=1/27$$. Therefore the tangent line is of the form $$y=\frac{1}{27}x+b$$. Plug in the point (27,3) we conclude that b=2. Therefore the tangent line is $$y=\frac{x}{27}+2$$. Now the estimate of of $$25^{1/3}$$ become $$\frac{25}{27}+2=\frac{79}{27}$$