16bf10lec2h

16bf10lec2h - Math 16b Thomas Scanlon Autumn 2010 Thomas...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

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: Math 16b Thomas Scanlon Autumn 2010 Thomas Scanlon Math 16b First derivative test for maxima/minima If f ( x ) is a function of one variable which has a relative maximum at a number a , then f ( a ) = 0. (Likewise, if f ( x ) has a relative minimum at a , then f ( a ) = 0.) Similarly, if F ( x , y ) is a function of two variables which has a relative extremum at some point ( a , b ) , then ∂ F ∂ x ( a , b ) = 0 and ∂ F ∂ y ( a , b ) = 0. Thomas Scanlon Math 16b An example Example Consider F ( x , y ) := x 2- 3 y 2 + xy +- x + 1 and nd where F may have a relative extremum. ∂ F ∂ x = 2 x + y- 1 ∂ F ∂ y =- 6 y + x Setting these equal to zero, we nd x = 6 y so that 13 y = 1 or y = 1 13 and x = 6 13 . Thomas Scanlon Math 16b Second derivative test Recall that if f ( x ) is a (su ciently di erentiable) function of a single variable and f ( a ) = 0 and f 00 ( a ) < 0, then f attains a local maximum at the point ( a , f ( a )) ....
View Full Document

{[ snackBarMessage ]}

Page1 / 12

16bf10lec2h - Math 16b Thomas Scanlon Autumn 2010 Thomas...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online