UseDefinition

UseDefinition - Mathematics 115 – F2011 Example Problem...

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Mathematics 115 – F2011 - Example Problem Let f (x) = √ x. (1) Use the definition of the derivative to find f (x): From the definition f (x + h) − f (x) f (x) = lim = lim h→0 h→0 h √ x+h− h √ x provided the limit exists. Simplify the difference quotient: √ √ √ √ √ √ x+h− x x+h− x x+h+ x = ·√ √ h h x+h+ x x+h−x =√ √ h( x + h + x ) 1 =√ √ x+h+ x Then. replacing the difference quotient with its simplified version, we get 1 1 f (x) = lim √ √=√ h→0 2x x+h+ x (2) What is the equation of the tangent line to the graph of f (x) = √ x at the point (4, 2). √ The line has slope f (4) = 1/2 4 = 1/4. So, the point-slope form of the line is y − 2 = f (2)(x − 4) = (1/4)(x − 4) and the y -intercept form is y = (1/4)x + 1 ...
View Full Document

This document was uploaded on 10/24/2011.

Ask a homework question - tutors are online