lecture24hout

lecture24hout - MATH 006 Calculus and Linear Algebra...

Info iconThis preview shows pages 1–6. 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 DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

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

Unformatted text preview: MATH 006 Calculus and Linear Algebra (Lecture 24) Albert Ku HKUST Mathematics Department Albert Ku (HKUST) MATH 006 1 / 16 Outline 1 Increasing and Decreasing Functions 2 Critical Values 3 Local Extrema 4 First-Derivative Test 5 Application Albert Ku (HKUST) MATH 006 2 / 16 Increasing and Decreasing Functions Definition Suppose y = f ( x ). 1 f ( x ) is increasing on an interval a < x < b , if for any a < x 1 < x 2 < b , f ( x 1 ) < f ( x 2 ). 2 f ( x ) is decreasing on an interval a < x < b , if for any a < x 1 < x 2 < b , f ( x 2 ) < f ( x 1 ). Albert Ku (HKUST) MATH 006 3 / 16 Increasing and Decreasing Functions Example Determine the interval for which the function f ( x ) = x 2 is increasing. Solution From the graph of y = x 2 , it is obvious that the function is increasing when x > 0 and decreasing when x < 0. Notice that the slope of the tangent is positive when f is increasing, and is negative when f is decreasing. Albert Ku (HKUST) MATH 006 4 / 16 Increasing and Decreasing Functions Theorem For the interval a < x < b, 1 f ( x ) is an increasing function on a < x < b if and only if f ( x ) > on a < x < b....
View Full Document

This note was uploaded on 12/28/2010 for the course MATH MATH006 taught by Professor Forgot during the Fall '09 term at HKUST.

Page1 / 16

lecture24hout - MATH 006 Calculus and Linear Algebra...

This preview shows document pages 1 - 6. Sign up to view the full document.

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