lecture11 - Lecture 11 1 Lecture 11: The Derivative of a...

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 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: Lecture 11 1 Lecture 11: The Derivative of a Function, Part II: (Sec. 2.6) Rates of Change, Differentiability Given a function y = f ( x ). The derivative of y with respect to x is the function f defined by: f ( x ) = Its domain: Lecture 11 2 The Slope of a Curve and the Derivative Def. The slope m of the graph of the curve y = f ( x ) at a given point ( x, f ( x )) is defined to be the slope of the tangent line to the curve at the point ( x, f ( x )) and is given by Lecture 11 3 The Derivative and Rates of Change ex. Let p ( x ) = 20 . 02 x be the demand function for a product. 1) Find the revenue function R ( x ). 100 200 300 400 500 600 700 800 900 1000 1000 2000 3000 4000 5000 R ( x ) = 2) Use the graph to estimate the rate at which rev- enue is changing when a) x = 100 b) x = 500 c) x = 900 Lecture 11 4 Consider again the revenue function R ( x ) = 20 x . 02 x 2 and the following table of val- ues: x 100 400 500 600 900 y 1800 4800 5000 4800 1800 1) What is the change in revenue as production in- creases from 100 to 400 units?...
View Full Document

This note was uploaded on 07/18/2011 for the course MAC 2233 taught by Professor Smith during the Spring '08 term at University of Florida.

Page1 / 18

lecture11 - Lecture 11 1 Lecture 11: The Derivative of a...

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