lecture24 - Math 006 (Lecture 24) Increasing and Decreasing...

Info iconThis preview shows pages 1–3. 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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 006 (Lecture 24) Increasing and Decreasing Functions Definition 1. Suppose y = f ( x ). 1. f ( x ) is increasing on the 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 the interval, a < x < b , if for any a < x 1 < x 2 < b , f ( x 2 ) ≤ f ( x 1 ). Example 1. Determine the interval for which the function f ( x ) = x 2 is increasing. Theorem 1. 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 . 2. f ( x ) is an decreasing function on a < x < b if and only if f ( x ) < on a < x < b . Example 2. Given the function f ( x ) = 8 x- x 2 , (a) Which values of x correspond to horizontal tangent line? (b) For which values of x is f ( x ) increasing? Decreasing? 1 Critical Values Definition 2. The values of x in the domain of f where 1. f ( x ) = 0, or 2. f ( x ) does not exist are called the critical values of f ....
View Full Document

Page1 / 5

lecture24 - Math 006 (Lecture 24) Increasing and Decreasing...

This preview shows document pages 1 - 3. Sign up to view the full document.

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