121616949-math.107

# 121616949-math.107 - 5 Curve Sketching Whether we are...

• Test Prep
• 1

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

5 Curve Sketching Whether we are interested in a function as a purely mathematical object or in connection with some application to the real world, it is often useful to know what the graph of the function looks like. We can obtain a good picture of the graph using certain crucial information provided by derivatives of the function and certain limits. A local maximum point on a function is a point ( x, y ) on the graph of the function whose y coordinate is larger than all other y coordinates on the graph at points “close to” ( x, y ). More precisely, ( x, f ( x )) is a local maximum if there is an interval ( a, b ) with a < x < b and f ( x ) f ( z ) for every z in ( a, b ). Similarly, ( x, y ) is a local minimum point if it has locally the smallest y coordinate. Again being more precise: (
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: x, f ( x )) is a local minimum if there is an interval ( a, b ) with a < x < b and f ( x ) ≤ f ( z ) for every z in ( a, b ). A local extremum is either a local minimum or a local maximum. Local maximum and minimum points are quite distinctive on the graph of a function, and are therefore useful in understanding the shape of the graph. In many applied problems we want to ﬁnd the largest or smallest value that a function achieves (for example, we might want to ﬁnd the minimum cost at which some task can be performed) and so identifying maximum and minimum points will be useful for applied problems as well. Some examples of local maximum and minimum points are shown in ﬁgure 5.1 . 93...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern