Class Notes (838,382)
Canada (510,868)
Mathematics (269)
MATH 157 (42)

7.1- First Derivative.pdf

7 Pages
Unlock Document

MATH 157
Chiaka Drake

1 Chapter 7.1 Applications of the First Derivative Introduction: In the next few lectures you will be introduced to skills and concepts that will allow you to __________ the graph of any function y f (x)by __________ without using _____________________ and answer questions of _________________ such as “What is the maximum profit for a certain business enterprise?”. Monotonicity: A function y f (x) is monotonic on an interval (a,b) if it is either __________ or __________ there. Suppose x 1 and x2 are in the interval and x1 x2. f is increasing if f (x ) f (x ); 1 2 f is decreasing if f (x1) f (x2). 2 Monotonicity Test: Suppose f is a _________________ function on an _________ interval (a,b) . If f (x) 0 for all x in(a,b) , then f is ____________________ on (a,b) . If f (x) 0 for all x in(a,b) , then f is ____________________ on (a,b) . If f (x) 0 for all x in(a,b) , then f is ____________________ on (a,b) . 3 Critical Numbers (x-values): for a function f are those ______________ c in the ______________ of f such that f (c) or f (c) (__________________). The points (c, f (c))are called ______________ points. Question: How can these intervals of increase and decrease be found? Answer: 1. Find all ______________ numbers of f and all numbers where f is ________________. Place these numbers on the real number line. This ______________ the number line into open intervals. 2. ______________ a number in __________ interval. 3. ______________ the _________________ Test to these numbers to decide if f is ______________ or ______________ on these intervals. Examples Q1: Given the demand function p 300x 2x 2, find when marginal revenue is increasing. 4 Q2: For h(x) x2/3. i) Find the domain. ii) Find all intervals of increase and dec
More Less

Related notes for MATH 157

Log In


Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.