3.9.1-eg - 2 / 3 . Since f (1) = (25 + 2 1) 1 / 3 = 27 1 /...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Example Find the linear approximation L ( x ) to the function f ( x ) = (25 + 2 x ) 1 / 3 at the point x = 1. Solution: Recall that for any differentiable function f , the linear approximation to f at the point x = x 0 is given by L ( x ) = f ( x 0 ) + f 0 ( x 0 )( x - x 0 ) , where in this case, f ( x ) = (25 + 2 x ) 1 / 3 and x 0 = 1 . Then f 0 ( x ) = 1 3 (25 + 2 x ) 1 / 3 - 1 · (25 + 2 x ) 0 = 1 3 (25 + 2 x ) - 2 / 3 · 2 = 2 3 (25 + 2 x )
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 2 / 3 . Since f (1) = (25 + 2 1) 1 / 3 = 27 1 / 3 = 3 , f (1) = 2 3 (25 + 2 1) 2 / 3 = 2 3 27 2 / 3 = 2 3 3 2 = 2 27 , it follows that the linear approximation of f ( x ) at x = 1 is L ( x ) = 3 + 2 27 ( x-1) ....
View Full Document

Ask a homework question - tutors are online