chapter4 - MATH1010: Chapter 4 cont 1 APPLICATIONS OF...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
MATH1010: Chapter 4 cont… 1 APPLICATIONS OF DERIVATIVES cont … Maximum and Minimum Values (Section 4.1, pg. 279) cont… Recall: Last day, we looked at max and min values, but we explored this concept graphically. Example: Sketch a graph of a continuous function f such that the absolute maximum of ) ( x f on the interval (-1, 1) does not exist and the absolute minimum equals 3. Recall: Last day, we discussed the Extreme Value Theorem which states that on a closed interval, a continuous function attains both an absolute max and an absolute min. Fermat’s Theorem: If f has a local maximum or minimum at c, and if ) ( c f exists, then 0 ) ( = c f . Caution: Some Important Points Are all places where the derivative is zero a local max/min?
Background image of page 1

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

View Full DocumentRight Arrow Icon
MATH1010: Chapter 4 cont… 2 Do local max/min occur only at places where the derivative is zero? Definition: A critical number of a function f is a number c in the domain of f such that either 0 ) ( = c f or ) ( c f does not exist. So, rephrasing
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 4

chapter4 - MATH1010: Chapter 4 cont 1 APPLICATIONS OF...

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